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## Usage

### Bidiagonalization

## See also

## References

## External links

In mathematics, a **bidiagonal matrix** is a banded matrix with non-zero entries along the main diagonal and *either* the diagonal above or the diagonal below. This means there are exactly two non zero diagonals in the matrix.

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**.

For example, the following matrix is **upper bidiagonal**:

and the following matrix is **lower bidiagonal**:

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

- 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.

**^**Bochkanov Sergey Anatolyevich. ALGLIB User Guide - General Matrix operations - Singular value decomposition . ALGLIB Project. 2010-12-11. URL:http://www.alglib.net/matrixops/general/svd.php. Accessed: 2010-12-11. (Archived by WebCite at https://www.webcitation.org/5utO4iSnR)

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

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