In the mathematical field of linear algebra, an arrowhead matrix is a square matrix containing zeros in all entries except for the first row, first column, and main diagonal.^[1] In other words, the matrix has the form

\begin{pmatrix} \,\! *&*&*&*&* \\ \,\! *&*&0&0&0 \\ \,\! *&0&*&0&0 \\ \,\! *&0&0&*&0 \\ \,\! *&0&0&0&* \end{pmatrix}.

Arrowhead matrices are used in some algorithms for finding of eigenvalues and eigenvectors.^[2]

References

1. ↑
2. ↑ M. Gu and S. C. Eisenstat (1995), "A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem," SIAM J. Matrix Anal. Appl., 16: 172-191.