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Vector Spaces and Subspaces

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

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.


Linear Algebra Library

Use only in the MuPAD Notebook Interface.

Numeric Algorithms Library

Use only in the MuPAD Notebook Interface.

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