Bidiagonal matrix

A bidiagonal matrix is a matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below.

For example, the following matrix is bidiagonal:

${\begin{pmatrix}1&4&0&0\\0&4&1&0\\0&0&3&4\\0&0&0&3\\\end{pmatrix}}$

When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal. When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal.

References

• Stewart, G. W. (2001) Matrix Algorithms, Volume II: Eigensystems. Society for Industrial and Applied Mathematics. ISBN 0-89871-503-2.