Documentation

# 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.

 `linalg::factorCholesky` The Cholesky decomposition of a matrix `linalg::factorLU` LU-decomposition of a matrix `linalg::factorQR` QR-decomposition of a matrix `linalg::frobeniusForm` Frobenius form of a matrix `linalg::hermiteForm` Hermite normal form of a matrix `linalg::inverseLU` Computing the inverse of a matrix using LU-decomposition `linalg::jordanForm` Jordan normal form of a matrix `linalg::smithForm` Smith normal form of a matrix `numeric::factorCholesky` Cholesky factorization of a matrix `numeric::factorLU` LU factorization of a matrix `numeric::factorQR` QR factorization of a matrix `numeric::singularvalues` Numerical singular values of a matrix `numeric::singularvectors` Numerical singular value decomposition of a matrix `numeric::svd` Numerical 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.

#### Mathematical Modeling with Symbolic Math Toolbox

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