Linear Algebra
Compute `aa = dd \ a * dd' in which `aa' is a matrix whose row and
column norms are roughly equal in magnitude, and `dd' = `p * d', in
which `p' is a permutation matrix and `d' is a diagonal matrix of
Compute the P-norm condition number of a matrix.
Compute the determinant of A using LAPACK for full and UMFPACK for
sparse matrices.
Scale a matrix by rows or columns, or a multidimensional tensor along a
specified dimension.
Computes the dot product of two vectors.
The eigenvalues (and eigenvectors) of a matrix are computed in a several
step process which begins with a Hessenberg decomposition, followed by a
Schur decomposition, from which the eigenvalues are ap
Return a 2 by 2 orthogonal matrix `G = [C S; -S' C]' such that `G [X;
Y] = [*; 0]' with X and Y scalars.
Given a two-element column vector, returns the 2 by 2 orthogonal matrix
G such that `Y = G * X' and `Y(2) = 0'.
Compute the inverse of the square matrix A.
Identify the matrix type or mark a matrix as a particular type.
Compute the p-norm of the matrix A.
Return an orthonormal basis of the null space of A.
Return an orthonormal basis of the range space of A.
Return the pseudoinverse of X.
Compute the rank of A, using the singular value decomposition.
Compute the 1-norm estimate of the reciprocal condition as returned by
LAPACK.
Compute the trace of A, `sum (diag (A))'.
Returns the reduced row echelon form of A.
Compute the Cholesky factor, R, of the symmetric positive definite
matrix A, where
Use the Cholesky factorization to compute the inverse of the symmetric
positive definite matrix A.
Invert a symmetric, positive definite square matrix from its Cholesky
decomposition, U.
Update or downdate a Cholesky factorization.
Compute the Hessenberg decomposition of the matrix A.
Compute the LU decomposition of A.
Compute the QR factorization of A, using standard LAPACK subroutines.
Given a QR factorization of a real or complex matrix A = Q*R, Q unitary
and R upper trapezoidal, return the QR factorization of A + U*V', where
U and V are column vectors (rank-1 update).
Given a QR factorization of a real or complex matrix A = Q*R, Q unitary
and R upper trapezoidal, return the QR factorization of
[A(:,1:j-1) x A(:,j:n)], where U is a column vector to be inserted into
Given a QR factorization of a real or complex matrix A = Q*R, Q unitary
and R upper trapezoidal, return the QR factorization of
[A(:,1:j-1) A(:,j+1:n)], i.
Generalized eigenvalue problem A x = s B x, QZ decomposition.
Compute the Hessenberg-triangular decomposition of the matrix pencil
`(A, B)', returning `AA = Q * A * Z', `BB = Q * B * Z', with Q and Z
orthogonal.
The Schur decomposition is used to compute eigenvalues of a square
matrix, and has applications in the solution of algebraic Riccati
equations in control (see `are' and `dare').
Determine the largest principal angle between two subspaces spanned by
columns of matrices A and B.
Compute the singular value decomposition of A
Compute Householder reflection vector HOUSV to reflect X to be the jth
column of identity, i.
Construct an orthogonal basis U of block Krylov subspace
Return the exponential of a matrix, defined as the infinite Taylor
series
Compute the matrix logarithm of the square matrix A.
Compute the matrix square root of the square matrix A.
Form the kronecker product of two matrices, defined block by block as
Solve the Sylvester equation