This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Matrix Decomposition

Cholesky, LU, and QR factorizations, singular value decomposition, Jordan, Frobenius, Hermite, and Smith forms of matrices

Note

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

To convert a MuPAD notebook file to a MATLAB live script file, see convertMuPADNotebook. MATLAB live scripts support most MuPAD functionality, although there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

MuPAD Functions

linalg::factorCholeskyThe Cholesky decomposition of a matrix
linalg::factorLULU-decomposition of a matrix
linalg::factorQRQR-decomposition of a matrix
linalg::frobeniusFormFrobenius form of a matrix
linalg::hermiteFormHermite normal form of a matrix
linalg::inverseLUComputing the inverse of a matrix using LU-decomposition
linalg::jordanFormJordan normal form of a matrix
linalg::smithFormSmith normal form of a matrix
numeric::factorCholeskyCholesky factorization of a matrix
numeric::factorLULU factorization of a matrix
numeric::factorQRQR factorization of a matrix
numeric::singularvaluesNumerical singular values of a matrix
numeric::singularvectorsNumerical singular value decomposition of a matrix
numeric::svdNumerical singular value decomposition of a matrix

Examples and How To

Compute Cholesky Factorization

The Cholesky factorization expresses a complex Hermitian (self-adjoint) positive definite matrix as a product of a lower triangular matrix L and its Hermitian transpose LH: A = LLH.

Compute LU Factorization

The LU factorization expresses an m×n matrix A as follows: P*A = L*U.

Compute QR Factorization

The QR factorization expresses an m×n matrix A as follows: A = Q*R.

Compute Factorizations Numerically

For numeric factorization functions, you can use the HardwareFloats, SoftwareFloats and Symbolic options.

Find Jordan Canonical Form of a Matrix

The Jordan canonical form of a square matrix is a block matrix in which each block is a Jordan block.

Concepts

Linear Algebra Library

Use only in the MuPAD Notebook Interface.

Numeric Algorithms Library

Use only in the MuPAD Notebook Interface.