Bidiagonal matrix

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 uses this method as well.