ztrans::addpattern
Add patterns for the Z transform
transform::fourier::addpatternAdd patterns for the Fourier transform
transform::invfourier::addpatternAdd patterns for the inverse Fourier transform transform::laplace::addpatterntransform::ztrans::addpatternProperties and Assumptions assume
Add patterns for the Laplace transform
transform::invlaplace::addpatternAdd patterns for the inverse Laplace transform
Add patterns for the Z transform
transform::invztrans::addpatternAdd patterns for the inverse Z transform
Define a property
assumeAlsoassuminggetprop
Define a property without removing prior assumptions Evaluate under assumptions
assumingAlsois
Evaluate under additional assumptions Query properties of expressions
Check a mathematical property of an expression Generic zero test
iszero
property::dependsproperty::haspropunassume
Dependence table with all properties of an expression Does an object have properties?
property::showprops
What assumptions are made? Delete the properties of an identifier
Linear Algebra
Matrix and Vector Construction array
Create an array
hfarrayCreate an array of hardware floats
densematrixdoprintmatrix
Create a matrix or a vector Print large matrices Create a matrix or a vector
linalg::hessenberglinalg::hessian
Hessenberg matrix
Hessian matrix of a scalar function Hilbert matrix
Inverse of a Hilbert matrix Inverse of a Pascal matrix
Jacobian matrix of a vector function Pascal matrix
linalg::hilbert
linalg::invhilbertlinalg::invpascallinalg::jacobian
linalg::pascal
linalg::randomMatrixlinalg::toeplitz
Generate a random matrix Toeplitz matrix
Vandermonde matrices and their inverses
12
linalg::vandermonde
linalg::invvandermondelinalg::wiedemann
Vandermonde matrices and their inverses Solving linear systems by Wiedemann's algorithm Matrix Operations and Transformations linalg::addCol
linalg::addRowlinalg::col
linalg::delCol
linalg::delRow
linalg::multCollinalg::multRowlinalg::row
linalg::setCol
linalg::setRow
linalg::swapCollinalg::swapRowinverse
transpose
htranspose
linalg::pseudoInversenumeric::inverselllint
norm
linalg::concatMatrixlinalg::crossProductlinalg::kroneckerProduct
linalg::normalizelinalg::ogCoordTab
linalg::orthog
linalg::scalarProductlinalg::stackMatrix
linalg::submatrixlinalg::substitutelinalg::sylvester
numeric::expMatrixnumeric::fMatrix
numeric::rotationMatrixlinalg::htransposelinalg::transpose
Linear combination of matrix columns
Linear combination of matrix rows Extract columns of a matrix Delete matrix columns
Delete matrix rows
Multiply columns with a scalar Multiply rows with a scalar Extract rows of a matrix Change a column of a matrix
Change a row of a matrix
Swap two columns in a matrix Swap two rows in a matrix Inverse of a matrix Transpose of a matrix
The Hermitean transpose of a matrix
Moore-Penrose inverse of a matrix Inverse of a matrix
Compute an LLL-reduced basis of a lattice
Compute the norm of a matrix, a vector, or a polynomial
Join matrices horizontally
Cross product of three-dimensional vectors
Kronecker product of matrices Normalize a vector
Table of orthogonal coordinate transformations Orthogonalization of vectors Scalar product of vectors Join matrices vertically
Extract a submatrix or a subvector from a matrix or a vector, respectively
Replace a part of a matrix by another matrix Sylvester matrix of two polynomials
Exponential of a matrix
Functional calculus for numerical square matrices
Orthogonal matrix of the rotation about an axis Hermitean transpose of a matrix Transpose of a matrix
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Matrix Analysis curldet
Curl of a vector field Determinant of a matrix
divergencegradienthessian
Divergence of a vector field Vector gradient
Hessian matrix of a scalar function Jacobian matrix of a vector function
jacobiannorm
laplacian
The Laplacian
Compute the norm of a matrix, a vector, or a polynomial
potentialThe (scalar) potential of a gradient field
vectorPotentialnumeric::det
Vector potential of a three-dimensional vector field Determinant of a matrix Adjoint of a matrix Angle between two vectors Characteristic matrix Condition number of a matrix
linalg::adjointlinalg::angle
linalg::charmatlinalg::cond
linalg::isHermiteanlinalg::isPosDeflinalg::ncols
Checks whether a matrix is Hermitean Test a matrix for positive definiteness Test whether a matrix is unitary Number of columns of a matrix
Number of non-zero elements of a matrix Number of rows of a matrix Permanent of a matrix Square root of a matrix Trace of a matrix Type specifier for vectors Curl of a vector field Determinant of a matrix Divergence of a vector field Vector gradient Vector gradient
linalg::isUnitary
linalg::nonZeros
linalg::nrows
linalg::permanent
linalg::sqrtMatrix
linalg::tr
linalg::vectorOf
linalg::curl
linalg::det
linalg::divergencelinalg::grad
linalg::gradient
linalg::laplacian
The Laplacian
linalg::potentialThe (scalar) potential of a gradient field
linalg::vectorPotentiallinalg::basis
Vector potential of a three-dimensional vector field Basis for a vector space
Vector Spaces and Subspaces
linalg::gaussElimlinalg::intBasis
Gaussian elimination
linalg::gaussJordan
Gauss-Jordan elimination
Basis for the intersection of vector spaces
14
linalg::matdim
Dimension of a matrix Number of rows of a matrix
linalg::nrows
linalg::nullspacelinalg::rank
Basis for the null space of a matrix Rank of a matrix
Basis for the sum of vector spaces Number of components of a vector Numerical estimate of the rank of a matrix linalg::sumBasis
linalg::vecdim
numeric::rank
Eigenvalues and Eigenvectors linalg::eigenvalues
linalg::eigenvectorsnumeric::eigenvalues
numeric::eigenvectorslinalg::jordanForm
numeric::spectralRadiusnumeric::spectralradiusMatrix Decomposition linalg::factorCholeskylinalg::factorLU
linalg::factorQR
linalg::frobeniusForm
linalg::hermiteFormlinalg::inverseLU
linalg::jordanFormlinalg::smithForm
numeric::factorCholeskynumeric::factorLU
numeric::factorQR
numeric::singularvaluesnumeric::singularvectors
numeric::svdLinear Equations det
norm
linalg::condlinalg::matlinsolvelinalg::matlinsolveLUlinalg::rank
linalg::toeplitzSolve
linalg::vandermondeSolve
Eigenvalues of a matrix
Eigenvectors of a matrix
Numerical eigenvalues of a matrix
Numerical eigenvalues and eigenvectors of a matrix Jordan normal form of a matrix
Spectral radius of a matrix Spectral radius of a matrix
The Cholesky decomposition of a matrix LU-decomposition of a matrix QR-decomposition of a matrix
Frobenius form of a matrix Hermite normal form of a matrix
Computing the inverse of a matrix using LU-decomposition Jordan normal form of a matrix Smith canonical form of a matrix
Cholesky factorization of a matrix LU factorization of a matrix QR factorization of a matrix
Numerical singular values of a matrix
Numerical singular value decomposition of a matrix Numerical singular value decomposition of a matrix Determinant of a matrix
Compute the norm of a matrix, a vector, or a polynomial
Condition number of a matrix
Solving systems of linear equations
Solving the linear system given by an LU decomposition Rank of a matrix
Solve a linear Toeplitz system
Solve a linear Vandermonde system
15
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