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Vector Spaces and Subspaces

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

MuPAD Functions

linalg::basisBasis for a vector space
linalg::gaussElimGaussian elimination
linalg::gaussJordanGauss-Jordan elimination
linalg::intBasisBasis for the intersection of vector spaces
linalg::matdimDimension of a matrix
linalg::nrowsNumber of rows of a matrix
linalg::nullspaceBasis for the null space of a matrix
linalg::orthogOrthogonalization of vectors
linalg::rankRank of a matrix
linalg::sumBasisBasis for the sum of vector spaces
linalg::vecdimNumber of components of a vector
numeric::rankNumerical 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.

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