User Guide

DescriptionCommand
Perform Gaussian elimination on a matrixGaussianElimination
Reduce a square matrix to Hessenberg formHessenbergForm
Construct a generalized Hilbert matrixHilbertMatrix
Test if a matrix is orthogonalIsOrthogonal
Compute the least-squares approximation to A . x = bLeastSquares
Solve the linear system A . x = bLinearSolve
Compute the inverse of a square matrix or pseudo-inverse of a non-
square matrix
MatrixInverse
Compute a QR factorization of a matrixQRDecomposition
Construct a random matrixRandomMatrix
Construct the Sylvester matrix of two polynomialsSylvesterMatrix
For information on arithmetic operations, see Matrix Arithmetic (page 146).
For information on selecting entries, subvectors, and submatrices, see Access-
ing Entries in Matrices and Vectors (page 144).
Example Determine a basis for the space spanned by the set of vectors {(2,
13, -15), (7, -2, 13), (5, -4, 9)}. Express the vector (25, -4, 9) with respect to
this basis.
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Find a basis for the vector space spanned by these vectors, and then construct
a matrix from the basis vectors.
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4.3 Linear Algebra • 151