LU decomposition of a rectangular matrix
LU decomposition of a rectangular matrix

QR decomposition of a rectangular matrix
QR decomposition of a rectangular matrix

LQ decomposition of a rectangular matrix
LQ decomposition of a rectangular matrix

Singular value decomposition
Singular value decomposition

Schur decomposition
Schur decomposition

Determinant
Calculation of the determinant

Matrix inverse
Calculation of the inverse matrix

Update of the inverse matrix by the Sherman-Morrison formula
Update of the inverse matrix by the Sherman-Morrison formula

Estimate of the condition number
Estimate of the condition number

Reduction of a general matrix to bidiagonal form
Reduction of a general matrix to bidiagonal form by the orthogonal transformation

Reduction of a square matrix to upper Hessenberg form
Reduction of a square matrix to upper Hessenberg form by the orthogonal transformation