In the field of linguistics , specifically in syntax , phonetic form abbreviated PF , refers to a certain level of mental representation of a linguistic expression, derived from surface structure , and related to Logical form linguistics logical form . Phonetic form is the level of representation wherein expressions, or sentences, are assigned a phonetic representation, which is then pronounced by the speaker. Phonetic form takes surface structure as its input, and outputs an audible or visual, in the case of sign languages , pronounced sentence. ref Ouhalla, J Introducing Transformational Grammar. 2nd Ed., page 68. Arnold Publishers, 1999 ref Notes references syntax stub Category Syntactic transformation ca Forma fon tica ... more details
A form filler is a software program that automatically fills forms in a user interface UI . Form fillers can be part of a larger program, like a password manager or a Single sign on enterprise single sign on E SSO solution. A form filler is the opposite of a Data scraping Screen scraping screen scraper , which extracts data from a form. See also Single sign on Enterprise single sign on OpenID Password manager Roboform LastPass Billeo External links http www.aformfiller.com A Freeware Form Filler for Windows http www.ietf.org rfc rfc3106 IETF RFC 3106 software type stub Category Communication software ... more details
Form 5 is an SEC filing submitted to the Securities and Exchange Commission on an annual basis by company officers, directors, or beneficial 10 owners, which summarizes their insider trading activities. This form is simply a combination of year s Form 4 filings, which are mandatory filings made shortly after insiders make transactions. Resources http www.sec.gov SEC Homepage Category SEC filings ... more details
Form 13F is a quarterly report of stock equity holdings by filed Institutional investor institutional investment managers with at least 100 million in equity assets under management of, as required by the United States Securities and Exchange Commission SEC . These investors include banks, insurance companies, hedge fund s, investment companies, foundations, and pension funds. Form 13F only reports long positions. Short positions are not required to be disclosed and are not reported. External links http www.sec.gov answers form13f.htm SEC Form 13F Information Category SEC filings ... more details
Unreferenced stub auto yes date December 2009 In software component component based programming Visual Basic , .NET framework .NET WinForms , and Borland Delphi Delphi , a form is an easy way to create a GUI window. A form contains components and controls, which are a high level representation of standard GUI widgets it s easier to manipulate the high level wrappers than to deal with the underlying API. At design time, visual controls buttons, text boxes, and the like and non visual components timers, database connections, and so on are placed on the form. These controls and components are moved and sized with a mouse, and their properties and event handler s are set with a special grid. At runtime, automatically generated code creates instances of these controls and components, and sets their properties. See also Form document Form web FormEngine Master detail Oracle Forms XForms Windows Forms Compu lang stub Categories DEFAULTSORT Form Programming Category GUI widgets Interwikis de Bildschirmmaske ... more details
Unreferenced date October 2008 See Kata for Form as used in the context of martial arts. Form is a specific way of performing a movement, often a strength training exercise, to avoid injury, prevent Cheating Strength training cheating and increase strength. Proper form Exercises or drills in sport have a recognized way of performing the movements that have two purposes Avoiding injury By using proper or good form, the risk of injury is lowered. A lack of proper form commonly results in injury or a lack of effect from the exercise being performed Maximize benefit Good form ensures that the movement only uses the main muscles, and avoids recruiting secondary muscles. As a muscle fatigues, the body attempts to compensate by recruiting other muscle groups and transferring force generation to non fatigued units. This reduces the benefits in strength or size gain experienced by the muscles as they are not worked to failure. External links http bodybuilding.about.com od injurypreventiontreatment tp trainingsafe.htm Category Physical exercise bodybuilding stub ... more details
Orphan date May 2008 In mathematics , the Laguerre form is generally given as a third degree tensor valued form, that can be written as, math mathfrak L w 1 2 D a 11 2 w 1 w 2 D a 12 w 2 2 D a 22 math . Category Tensors math stub ... more details
Intersection form may refer to Intersection theory mathematics intersection form 4 manifold disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
Ternary form , sometimes called song form , ref name HD2nd binary and ternary is a three part musical form , usually schematicized as A B A. The first and third parts A are musically identical, or very nearly so, while the second part B in some way provides a contrast with them. The B section is often called the trio music trio , especially in minuet s and scherzo scherzi . ref name HD2nd trio 2 Examples include Robert Schumann Schumann s Folk Song , Album for the Young Op. 68, No. 9 and Fr d ric ... . The Analysis of Music , p.53 54. ISBN 0 13 033233 X. ref Characteristics of the form In ternary form, unlike the rounded binary form , each section will usually be self contained both theme music ... made by whom? date August 2011 between compound ternary form in which each large part of the form is itself divided in a way to suggest ternary or binary form giving, for example, an overall scheme of Nowrap A B A C D C A B A and simple ternary form , in which each large part of the form has no particular structure itself. Da capo aria Da capo arias are usually in simple ternary form minuets or scherzos and trios are normally compound. Another name for the latter is composite ternary form . citation needed date August 2011 The repetition of any section results in expanded ternary form . ref name ... 2011 Usage As well as in marches, ternary form is often found in baroque music baroque opera aria s the da capo aria and in many dance forms, such as polka s. It is also the form used in the minuet or scherzo ... 2011 See also Thirty two bar form Sources reflist refs ref name HD2nd binary and ternary Binary and ternary form in the Harvard Dictionary of Music , 2nd ed. rev. and enlarged 1969 . Willi Apel, ed ... links http www.artofcomposing.com 06 ternary form Small Ternary Form www.artofcomposing.com Category Musical form Category Song forms musical form ca Forma tern ria es Forma ternaria fr Forme ternaire ... Ternary form uk zh ... more details
In mathematics , a volume form on a differentiable manifold is a nowhere vanishing differential form of top degree. Thus on a manifold M of dimension n , a volume form is an n form, a section fiber bundle ... , that is nowhere equal to zero. A manifold has a volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a non vanishing function yields another volume form. On non orientable manifolds, one may instead define the weaker notion of a Density on a manifold density . A volume form provides a means to define the integral of a Function mathematics function on a differentiable manifold. In other words, a volume form gives ... Lebesgue integral . The absolute value of a volume form is a volume element , which is also known variously as a twisted volume form or pseudo volume form . It also defines a measure, but exists ... oriented, and so possess a volume form. More generally, the n sup th sup exterior power of the symplectic form on a symplectic manifold is a volume form. Many classes of manifolds have canonical volume forms they have extra structure which allows the choice of a preferred volume form. Oriented ... form. Orientation A manifold is orientable if it has a coordinate atlas all of whose transition functions ... . A volume form &omega on M gives rise to an orientation in a natural way as the atlas of coordinate charts on M that send &omega to a positive multiple of the Euclidean volume form math dx 1 wedge cdots wedge dx n math . A volume form also allows for the specification of a preferred class of moving ... in n dimensions with positive determinant. They form a principal bundle principal GL sup sup n sub bundle of the linear frame bundle of M , and so the orientation associated to a volume form gives a canonical ... that a volume form gives rise to G structure GL sup sup n structure on M . More reduction ... 1 Thus a volume form gives rise to an SL n structure as well. Conversely, given an SL n structure ... more details
refimprove date December 2007 Generally, in mathematics , a canonical form often called normal form or standard form of an object is a standard way of presenting that object. Canonical form can also mean a differential form that is defined in a natural canonical way Differential forms see below . Finding a canonical form is called canonization . In some branches of computer science the term canonicalization ... . A canonical form is given by designating some objects of S to be in canonical form , such that every object under consideration is equivalent to exactly one object in canonical form. In other words ... objects are equivalent, it then suffices to test their canonical forms for equality. A canonical form ... a given object s in S to its canonical form s ? Canonical forms are generally used to make operating with equivalence classes more effective. For example in modular arithmetic , the canonical form for a residue ... . A canonical form may simply be a convention, or a deep theorem. For example, polynomials are conventionally ... of Jordan canonical form for a matrix is a deep theorem. Examples Note in this section, up to some equivalence relation E means that the canonical form is not unique in general, but that if one ... A is equivalent to B if Normal form Notes Normal matrix Normal matrices over the complex numbers ... normal form up to reordering of blocks Matrices over a field math A P 1 B P math for some invertible matrix P Frobenius normal form Matrices over a principal ideal domain math A P 1 B Q math for some invertible Matrices P and Q Smith normal form The equivalence is the same as allowing invertible ... form Conjunctive normal form Disjunctive normal form Algebraic normal form Canonical form Boolean algebra Prenex normal form Skolem normal form Functional analysis class wikitable Objects A is equivalent to B if Normal form Hilbert spaces A and B are isometrically isomorphic as Hilbert spaces math ... theory canonical representation of a positive integer canonical form of a continued fraction Algebra ... more details
Unreferenced date December 2009 A form is a Class education class or grouping of students in a school . The term is used predominantly in the United Kingdom , although some schools, mostly Private school private , in other countries also use the title. Pupils are usually grouped in forms according to age and will remain with the same group for a number of years, or sometimes their entire school career. Forms are normally identified by a number such as first form or sixth form . A form number may be used for two year groups and differentiated by the terms upper and lower. The sixth form is the senior form of a school, and is usually divided into two year groups the lower sixth and upper sixth. If there is more than one form for each year group they will normally be differentiated by the letters A to D or X, Y, L and M. As in upper four B , lower two Y . Schools are frequently eccentric in how they name forms and do not follow a consistent pattern. Another common identification for form, and one of the most common in New Zealand , is the number of the year they are in, followed by the cypher US initials of the teacher who takes the form class e.g. 11JS would be a Year 11 class, who the form teacher is John Smith cypher JS . In some older schools, especially the older grammar school s and state school s, some forms are not given numbers but traditional names such as shell education shell and remove education remove . DEFAULTSORT Form Education Category Education in the United Kingdom Category Education in Canada Category Education in Barbados Category Educational stages Category Educational years de Schulklasse ... more details
Form N 1A is a registration statement used by investment companies to create new open end mutual funds . A company must file this form with the Securities and Exchange Commission s EDGAR filing system. Companies file an N 1A under the Investment Company Act of 1940 if they wish to register shares of the mutual fund. They file it under the Securities Act of 1933 if they wish to offer shares to customers. References http www.sec.gov about forms formn 1a.pdf PDF of Form N 1A http www.sec.gov info edgar forms edgform.pdf Form Types Used for Electronic Filing on EDGAR Category SEC filings econ stub ... more details
Unreferenced stub auto yes date December 2009 A form letter is a Letter message letter written from a template, rather than being specially composed for a specific recipient. The most general kind of form letter consists of one or more regions of Boilerplate text boilerplate text interspersed with one or more substitution placeholders . Although form letters are generally intended for a wide audience, many form letters include stylistic elements or features intended to appear specifically tailored to the recipient &mdash for example, they might be signed by autopen and utilize features such as mail merge to automatically insert the names of individual recipients. Computer A letter created for printing and distribution to a group of people whose names and addresses are taken from a database and inserted by a mail merge program into a single basic document. Uses Form letters are often used as replies from people who get large amounts of correspondence, such as celebrity celebrities or politician s. Other form letters are used to notify candidates as part of an application process, such as acceptance or rejection letter s from publishing companies, colleges or prospective employers. See also E mail spam DEFAULTSORT Form Letter Category Letters message Lit stub ... more details
unreferenced date May 2011 Form grabbing is an advanced Crimeware based method of capturing web form data within various browsers. Often confused with traditional keylogging recording individual keystrokes , this method intercepts the on submit API in browsers and collects web form data before it passes over the internet. Other methods of form grabbing function similarly using a web browser Plug in computing add on or malicious toolbar to automatically read the information in log in forms when the client submits it. This type of method is very effective in recording online banking passwords and other sensitive data because it only records log in, password, IP address , URL and other form fields based on what the attacker specifies. This is a growing type of computer based security attack. The most used form grabber is Zeus trojan horse Zeus . The first versions were sold in 2007 and since then it has grown to a share of almost 90 of all password stealing trojans. Its biggest rival is Spy Eye which started as a cheaper alternative to Zeus but stopped being sold in public in late 2009. Form grabbing was invented in 2003 with the Berbew Trojan believed to be created by Smash. References reflist Category Hacking computer security Category Malware Category Web security exploits malware stub web stub fr R cup ration de formulaire ... more details
Form S 1 is an SEC filing used by public companies to register their securities with the U.S. Securities and Exchange Commission SEC as the registration statement under the Securities Act of 1933 . The S 1 contains the basic business and financial information on an issuer with respect to a specific securities offering. Investors may use the prospectus finance prospectus to consider the merits of an offering and make educated investment decisions. A prospectus is one of the main documents used by an investor to research a company prior to an initial public offering IPO . Other less detailed registration forms, such as Form S 3 may be used for certain registrations. Every business day from 10 to 5, S 1 forms are filed with the SEC s EDGAR EDGAR filing system , the required filing format of the U.S. Securities and Exchange Commission. However many of these typically 30 to 90 are of the related Form S 1 A, which is used for filing amendments to a previously filed Form S 1. The S 1 form has an OMB Approval Number of 3234 0065 and the online form is only 8 pages. However the simplicity of the form s design is belied by the Office of Management and Budget OMB Office s figure of the Estimated Average Burden 972.32 hours. This means that long time and effort has been used to collect and display information about the filer a corporate registrant or new registrant who intends to offer securities . The S 1 form requires that the registrant provide information from diverse sources and incorporate this information using many rules or regulations, such as General Rules and Regulations under the Securities Act, Regulation C, Regulation S K and Regulation S X. References http www.sec.gov about forms forms 1.pdf PDF of Form S 1 http www.sec.gov info edgar forms edgform.pdf Form Types Used for Electronic Filing on EDGAR External links http secwatch.com s1 Latest S 1 Filings Category SEC filings econ stub ... more details
In mathematics , a Riemann form in the theory of abelian varieties and modular forms , is the following data A Lattice group Lattices in complex space lattice in a complex vector space C sup g sup . An bilinear form alternating bilinear form from to the integer s satisfying the following Riemann bilinear relations ol li the real linear extension sub R sub C sup g sup C sup g sup R of satisfies sub R sub iv , iw sub R sub v , w for all v , w in C sup g sup C sup g sup li the associated hermitian form H v , w sub R sub iv , w i sub R sub v , w is definite bilinear form positive definite . ol The hermitian form written here is linear in the first variable. Riemann forms are important because of the following The alternatization of the Chern class of any factor of automorphy is a Riemann form. Conversely, given any Riemann form, we can construct a factor of automorphy such that the alternatization of its Chern class is the given Riemann form. References Citation last Milne first James title Abelian Varieties year 1998 url http www.jmilne.org math CourseNotes av.html accessdate 2008 01 15 Citation last Hindry first Marc last2 Silverman first2 Joseph H. title Diophantine Geometry, An Introduction publisher location New York series Graduate Texts in Mathematics isbn 0 387 98981 1 id MathSciNet id 1745599 year 2000 volume 201 Citation last Mumford first David author link David Mumford title Abelian Varieties publisher Oxford University Press location London series Tata Institute of Fundamental Research Studies in Mathematics id MathSciNet id 0282985 year 1970 volume 5 Springer title Abelian function id A a010220 Springer title Theta function id T t092600 DEFAULTSORT Riemann Form Category Abelian varieties ... more details
Orphan date September 2006 att April 2011 Wikify date September 2009 Form 10 12B is a U.S. SEC filing used to register securities pursuant to Section 12 b of the Securities Exchange Act of 1934 in the United States . Form Uses This form is one of the most useful of the security registration forms because it relates to securities created as a result of a spin off. Reading the Form There are three major portions of the 10 12B form Letter to Shareholders from Parent Company This provides a history of the parent company, their reason for the spin off, and other relevant information. Information Statement This section contains all the information investors need to know. Occasionally, portions of this section will be left blank and amended with 10 12B A filings at a later time. Financial Information This section contains all the financial information, including pro forma statements. These statements show what the financials would look like if the spun off division were its own company in the past. Resources Official http www.sec.gov Category SEC filings ... more details
In mathematics , a sesquilinear form on a complex vector space V is a map V × V &rarr C that is linear ... prefix Wiktionary sesqui sesqui meaning one and a half . Compare with a bilinear form , which ... &isin V and all a , b &isin C . A sesquilinear form can also be viewed as a complex bilinear map math ... phi w,z math is a conjugate linear functional on V . Given any sesquilinear form &phi on V we can define a second sesquilinear form &psi via the conjugate transpose math psi w,z overline varphi z,w . math ... form can be written as a sum of a Hermitian form and a skew Hermitian form. Geometric motivation ... 2 sup z sup sup z . The norm associated to a sesquilinear form is invariant under multiplication by the complex circle complex numbers of unit norm , while the norm associated to a bilinear form is equivariant ... forms are geometrically more natural. If B is a bilinear form on a complex vector space and math ... form on a complex vector space and math x S S x,x math is the associated norm, then math ix S S ix,ix bar i i S x,x x S math . Hermitian form The term Hermitian form may also refer to a different concept than that explained below it may refer to a certain differential form on a Hermitian manifold . A Hermitian form also called a symmetric sesquilinear form , is a sesquilinear form h V × V &rarr C such that math h w,z overline h z, w . math The standard Hermitian form on C ... product on any complex Hilbert space is a Hermitian form. A vector space with a Hermitian form ... algebra basis e sub i sub of V , a Hermitian form is represented by a Hermitian matrix H math ... , e sub j sub . The quadratic form associated to a Hermitian form Q z h z , z is always real number real . Actually one can show that a sesquilinear form is Hermitian iff the associated quadratic form is real for all z &isin V . Skew Hermitian form A skew Hermitian form also called an antisymmetric sesquilinear form , is a sesquilinear form &epsilon V × V &rarr C such that math varepsilon ... more details
form is one for which the associated matrix is non singular matrix non singular , and accordingly ... form s. Symmetric nondegenerate forms are important generalizations of inner products ... manifold , while relaxing this to a symmetric nondegenerate form yields a pseudo Riemannian manifold . Infinite dimensions Note that in an infinite dimensional space, we can have a bilinear form for which ... of continuous function s on a closed bounded interval, the form math f phi, psi int psi x phi x dx ... form. On the other hand, this bilinear form satisfies math f phi, psi 0 , math for all math ... to be totally degenerate . Given any bilinear form on V the set of vectors math x in V mid ... math x in V math such that math f x,x 0 math is called isotropic for the isotropic quadratic form quadratic form associated with the bilinear form math f math and the existence of isotropic lines does not imply that the form is degenerate. Category Bilinear forms fa pl Forma dwuliniowa ... more details
Hatnote This article is about the term as used in logic. For the linguistics term, see Logical Form In logic the logical form of a sentence or proposition or wikt statement statement or truthbearer or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form. In an ideal logical language, the logical form can be determined from syntax alone formal languages used in formal science s are examples of such languages. Logical form however should not be confused with the mere syntax used ... logical form in a given language. ref The Cambridge Dictionary of Philosophy, CUP 1999, pp. 511 512 ref The logical form of an argument is called the argument form or test form of the argument . History That the concept of form is fundamental to logic was already recognized in ancient times. Aristotle ... of the argument. The term logical form was introduced by Bertrand Russell in 1914, in the context ... cite book editor Gerhard Preyer, Georg Peter title Logical form and language url http books.google.com ... 54 chapter What is logical form? author Ernie Lepore, Kirk Ludwig http www.indiana.edu socrates papers What 20is 20Logical 20Form.pdf preprint ref Example of argument form To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences ... is mortal. Argument Form All H are M . S is H . Therefore, S is M . All we have done in the Argument form is to put H for human and humans , M for mortal , and S for Socrates what results is the form of the original argument. Moreover, each individual sentence of the Argument form is the sentence form of its respective sentence in the original argument. ref cite book last Hurley first Patrick ... 1988 isbn 0534089283 ref Importance of argument form Attention is given to argument and sentence form, because form is what makes an argument validity valid or cogency cogent . Some examples of valid ... more details
about reduced form in econometrics the reduced form of a fraction Irreducible fraction Unreferenced date December 2009 In statistics , and particularly in econometrics , the reduced form of a system of equations ... the latter as a function of the exogenous variables, if any. In econometrics, structural form models begin from deductive theories of the economy, while reduced form models begin by identifying ... expression of a structural form is math f Y, X, varepsilon 0 math , where f is a function, possibly from vectors to vectors in the case of a multiple equation model. The reduced form of this model is given by math Y g X, varepsilon math , with g a function. Structural form As an example ... D P , math with positive b sub S sub and negative b sub D sub . This is the structural form of the equation .... Reduced form To find the reduced form, one must system of linear equations Solving a linear ... are the reduced form coefficients. They are easily identified from data on Q and P . However, the four structural form coefficients above can not be identified from data the parameter identification problem ... by an exogenous variable, Z . The structural form becomes supply math Q a S b S P .... This structural model can be rewritten in the reduced form math Q pi 10 pi 11 Z , math math P pi 20 pi 21 Z , math As before, the four reduced form math pi math coefficients can be derived from the five structural form coefficients. Note that both endogenous variables depend on the exogenous variable Z . By combining the two reduced form equations to eliminate Z , the structural coefficients of the supply side model math a S math and math b S math can be derived from the four reduced form coefficients ... are matrix mathematics matrices A is a square M × M matrix. The reduced form of the system ... . The M reduced form equations the rows of the matrix equation y x above can be identified from the data ... form to the reduced form, a coherence condition coherency condition might be needed to ensure the reduced ... more details
orphan date July 2009 Form 8850 is a United States Internal Revenue Service IRS tax form entitled Pre Screening Notice and Certification Request for the Work Opportunity Credit . The form is used in implementation of the federal government of the United States federal government s Work Opportunity Tax Credit program, which provides federal tax credit s as incentives for employers of low income youth participating in summer work programs, former welfare recipients, food stamp recipients, people referred from vocational rehabilitation programs, military veterans, ex felons, and people receiving Supplemental Security Income . ref name DOL http www.dol.gov odep pubs fact wotc.htm Work Opportunity Tax Credit Program , U.S. Department of Labor website, accessed August 13, 2011 ref Although it is an IRS form, Form 8850 is filed with the U.S. state state workforce or employee security agency to request certification that a newly hired employee is a member of an eligible group. ref name DOL ref http www.irs.gov pub irs pdf i8850.pdf IRS Instructions for Form 8850 , accessed August 13, 2011 ref Employers are required to complete the form to be eligible for Chicago City of Chicago tax incentives to employ the city s Welfare to Work participants. Citation needed date August 2011 See also Personal Responsibility and Work Opportunity Act References reflist External links http www.irs.gov pub irs pdf f8850.pdf Form 8850 at the IRS website http www.irs.gov pub irs pdf i8850.pdf IRS Instructions for Form 8850 tax stub Category United States government forms 8850 Category Internal Revenue Service Category Federal assistance in the United States Category Tax forms ... more details
In differential geometry , the curvature form describes curvature of a connection form connection on a principal bundle . It can be considered as an alternative to or generalization of curvature tensor in Riemannian geometry . Definition Let G be a Lie group with Lie algebra math mathfrak g math , and P B be a principal bundle principal G bundle . Let be an Ehresmann connection on P which is a math mathfrak g math valued Differential form one form on P . Then the curvature form is the math mathfrak g math valued 2 form on P defined by math Omega d omega 1 over 2 omega, omega D omega. math Here math d math stands for exterior derivative , math cdot, cdot math is defined by math alpha otimes X, beta otimes Y alpha wedge beta otimes X, Y mathfrak g math and D denotes the exterior covariant derivative . In other terms, math , Omega X,Y d omega X,Y omega X , omega Y . math Curvature form in a vector ... 1 form and each math Omega i j math is a usual 2 form then math Omega i j d omega i j sum k omega i ... group is O n and is a 2 form with values in o n , the skew symmetric matrix antisymmetric matrices . In this case the form is an alternative description of the Riemann curvature tensor curvature ... tensor, Bianchi identities If math theta math is the canonical vector valued 1 form on the frame bundle, the Connection form Torsion torsion math Theta math of the connection form math omega math is the vector valued 2 form defined by the structure equation math Theta d theta omega wedge theta D theta, math where as above D denotes the Connection form Exterior covariant derivative exterior covariant derivative . The first Bianchi identity takes the form math D Theta Omega wedge theta. math The second Bianchi identity takes the form math , D Omega 0 math and is valid more generally for any Connection form Connection connection in a principal bundle . References S.Kobayashi and K.Nomizu, Foundations ... principal bundle Basic introduction to the mathematics of curved spacetime Chern Simons form Curvature ... more details
In multilinear algebra , a multilinear form is a Map mathematics map of the type math f V n to bold K , math where V is a vector space over the field mathematics field K , that is separately linear in each its n variables. ref MathWorld title Multilinear Form urlname MultilinearForm ref For n 2, i.e. only two variables, one calls a bilinear form . An important type of multilinear forms are alternating multilinear forms which have the additional property of changing their sign under exchange of two arguments. When K has characteristic algebra characteristic other than 2, this is equivalent to saying that math f dots,x, dots,x, dots 0 , math i.e. the form vanishes if supplied the same argument twice. The exceptional case of characteristic 2 requires more care. Special cases of these are determinant forms and differential form s. See also Homogeneous polynomial References Reflist DEFAULTSORT Multilinear Form Category Multilinear algebra cs Multiline rn forma de Multilinearform es Forma multilineal fr Forme multilin aire pt Fun o n linear zh ... more details
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