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: Usage One variant of the QR algorithm starts with reducing a general matrix into a bidiagonal one, and the singular value decomposition (SVD) uses this method as well. Bidiagonalization Bidiagonalization allows guaranteed accuracy when using floating-point arithmetic to compute singular values. See also List of matrices LAPACK Hessenberg form – The Hessenberg form is similar, but has more non-zero diagonal lines than 2. References Stewart, G. W. (2001) Matrix Algorithms, Volume II: Eigensystems. Society for Industrial and Applied Mathematics. . External links High performance algorithms for reduction to condensed (Hessenberg, tridiagonal, bidiagonal) form Linear algebra Sparse matrices