2015年6月13日 星期六

MuPAD--linalg函數庫(linear algebra package)中的函數

可鍵入info(linalg)觀察在linalg(linear algebra package)函數庫中的函數; 也可以由MuPAD 的Help查詢更詳細的使用說明

[[From MuPAD Help]]

linalg::addCol – linear combination of matrix columns
linalg::addRow – linear combination of matrix rows
linalg::adjoint – Adjoint of a matrix
linalg::angle – The angle between two vectors
linalg::basis – basis for a vector space
linalg::charmat – characteristic matrix
linalg::charpoly – characteristic polynomial of a matrix
linalg::col – extract columns of a matrix
linalg::companion – Companion matrix of a univariate polynomial
linalg::concatMatrix – join matrices horizontally
linalg::cond – Condition number of a matrix
linalg::crossProduct – cross product of three-dimensional vectors
linalg::curl – curl of a vector field
linalg::delCol – delete matrix columns
linalg::delRow – delete matrix rows
linalg::det – determinant of a matrix
linalg::divergence – divergence of a vector field
linalg::eigenvalues – eigenvalues of a matrix
linalg::eigenvectors – eigenvectors of a matrix
linalg::expr2Matrix – construct a matrix from equations
linalg::factorCholesky – the Cholesky decomposition of a matrix
linalg::factorLU – LU-decomposition of a matrix
linalg::factorQR – QR-decomposition of a matrix
linalg::frobeniusForm – Frobenius form of a matrix
linalg::gaussElim – Gaussian elimination
linalg::gaussJordan – Gauss-Jordan elimination
linalg::gradient, linalg::grad – vector gradient
linalg::hermiteForm – Hermite normal form of a matrix
linalg::hessenberg – Hessenberg matrix
linalg::hessian – Hessian matrix of a scalar function
linalg::hilbert – Hilbert matrix
linalg::htranspose – Hermitean transpose of a matrix
linalg::intBasis – basis for the intersection of vector spaces
linalg::inverseLU – computing the inverse of a matrix using LU-decomposition
linalg::invhilbert – inverse of a Hilbert matrix
linalg::invpascal – inverse of a Pascal matrix
linalg::isHermitean – checks whether a matrix is Hermitean
linalg::isPosDef – test a matrix for positive definiteness
linalg::isUnitary – test whether a matrix is unitary
linalg::jacobian – Jacobian matrix of a vector function
linalg::jordanForm – Jordan normal form of a matrix
linalg::kroneckerProduct – Kronecker product of matrices
linalg::laplacian – the Laplacian
linalg::matdim – dimension of a matrix
linalg::matlinsolve – solving systems of linear equations
linalg::matlinsolveLU – solving the linear system given by an LU decomposition
linalg::minpoly – minimal polynomial of a matrix
linalg::multCol – multiply columns with a scalar
linalg::multRow – multiply rows with a scalar
linalg::ncols – number of columns of a matrix
linalg::nonZeros – number of non-zero elements of a matrix
linalg::normalize – normalize a vector
linalg::nrows – number of rows of a matrix
linalg::nullspace – basis for the null space of a matrix
linalg::ogCoordTab – table of orthogonal coordinate transformations
linalg::orthog – orthogonalization of vectors
linalg::pascal – Pascal matrix
linalg::permanent – permanent of a matrix
linalg::potential – the (scalar) potential of a gradient field
linalg::pseudoInverse – Moore-Penrose inverse of a matrix
linalg::randomMatrix – generate a random matrix
linalg::rank – rank of a matrix
linalg::row – extract rows of a matrix
linalg::scalarProduct – scalar product of vectors
linalg::setCol – change a column of a matrix
linalg::setRow – change a row of a matrix
linalg::smithForm – Smith canonical form of a matrix
linalg::sqrtMatrix – square root of a matrix
linalg::stackMatrix – join matrices vertically
linalg::submatrix – extract a submatrix or a subvector from a matrix or a vector, respectively
linalg::substitute – replace a part of a matrix by another matrix
linalg::sumBasis – basis for the sum of vector spaces
linalg::swapCol – swap two columns in a matrix
linalg::swapRow – swap two rows in a matrix
linalg::sylvester – Sylvester matrix of two polynomials
linalg::tr – trace of a matrix
linalg::toeplitz – Toeplitz matrix
linalg::toeplitzSolve – solve a linear Toeplitz system
linalg::transpose – transpose of a matrix
linalg::vandermonde, linalg::invvandermonde – Vandermonde matrices and their inverses
linalg::vandermondeSolve – solve a linear Vandermonde system
linalg::vecdim – number of components of a vector
linalg::vectorOf – type specifier for vectors
linalg::vectorPotential – vector potential of a three-dimensional vector field
linalg::wiedemann – solving linear systems by Wiedemann's algorithm

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