Bidiagonal matrix

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A

So that means there are two non zero diagonal in the matrix.

When the diagonal above the main diagonal has the non-zero entries the matrix is

For example, the following matrix is

and the following matrix is

starts with reducing a general matrix into a bidiagonal one.

and the Singular value decomposition

uses this method as well.

**bidiagonal matrix**is a matrix with non-zero entries along the main diagonal and*either*the diagonal above or the diagonal below.So that means there are two non zero diagonal 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**:## Usage

One variant of the QR algorithmQR algorithm

In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR transformation was developed in the late 1950s by John G.F. Francis and by Vera N. Kublanovskaya , working independently...

starts with reducing a general matrix into a bidiagonal one.

and the Singular value decomposition

Singular value decomposition

In linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....

uses this method as well.

## See also

- Diagonal matrixDiagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The diagonal entries themselves may or may not be zero...
- List of matrices
- LAPACKLAPACK-External links:* : a modern replacement for PLAPACK and ScaLAPACK* on Netlib.org* * * : a modern replacement for LAPACK that is MultiGPU ready* on Sourceforge.net* * optimized LAPACK for Solaris OS on SPARC/x86/x64 and Linux* * *...
- BidiagonalizationBidiagonalizationBidiagonalization is one of unitary matrix decompositions such that U* A V = B, where U and V are unitary matrices; * denotes Hermitian transpose; and B is upper bidiagonal...
- Hessenberg form The Hessenberg form is similar, but has more non zero diagonal lines than 2.
- Tridiagonal matrix with three diagonals

## External links

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