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Bidiagonal matrix

For example, the following matrix is upper bidiagonal:

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

and the following matrix is lower bidiagonal:

${\displaystyle {\begin{pmatrix}1&0&0&0\\2&4&0&0\\0&3&3&0\\0&0&4&3\\\end{pmatrix}}.}$

One variant of the QR algorithm starts with reducing a general matrix into a bidiagonal one,^[1] and the singular value decomposition (SVD) uses this method as well.

Bidiagonalization allows guaranteed accuracy when using floating-point arithmetic to compute singular values.^[2]

This section needs expansion. You can help by adding to it. (January 2017)

• List of matrices
• LAPACK
• Hessenberg form – The Hessenberg form is similar, but has more non-zero diagonal lines than 2.

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

• High performance algorithms for reduction to condensed (Hessenberg, tridiagonal, bidiagonal) form

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