Documentation

# Vector Spaces and Subspaces

Matrix dimensions, rank, null space, reduced row echelon form

### 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::basis` Basis for a vector space `linalg::gaussElim` Gaussian elimination `linalg::gaussJordan` Gauss-Jordan elimination `linalg::intBasis` Basis for the intersection of vector spaces `linalg::matdim` Dimension of a matrix `linalg::nrows` Number of rows of a matrix `linalg::nullspace` Basis for the null space of a matrix `linalg::orthog` Orthogonalization of vectors `linalg::rank` Rank of a matrix `linalg::sumBasis` Basis for the sum of vector spaces `linalg::vecdim` Number of components of a vector `numeric::rank` Numerical estimate of the rank of a matrix

## Examples and How To

Compute Dimensions of a Matrix

To find the dimensions of a matrix, use the `linalg::matdim` command.

Compute Reduced Row Echelon Form

For the reduced row echelon form of a matrix, the following conditions are valid:

Compute Rank of a Matrix

The rank of a matrix is the number of independent rows of a matrix.

Compute Bases for Null Spaces of Matrices

Find null space of matrix.

## 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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