Matrix Operations

The Wolfram Language's matrix operations handle both numeric and symbolic matrices, automatically accessing large numbers of highly efficient algorithms. The Wolfram Language uses state-of-the-art algorithms to work with both dense and sparse matrices, and incorporates a number of powerful original algorithms, especially for high-precision and symbolic matrices.

(RefLink[+, paclet:ref/Plus]), (RefLink[*, paclet:ref/Times]), (RefLink[^, paclet:ref/Power]), ... — all automatically work element-wise

(RefLink[Dot, paclet:ref/Dot]) ((RefLink[., paclet:ref/Dot])) — products of matrices, automatically handling row and column vectors

(RefLink[Inverse, paclet:ref/Inverse]) — matrix inverse (use (RefLink[LinearSolve, paclet:ref/LinearSolve]) for linear systems)

(RefLink[Transpose, paclet:ref/Transpose]) — transpose (mᵀ, entered with (Key0[esc]) tr (Key0[esc]))

(RefLink[ConjugateTranspose, paclet:ref/ConjugateTranspose]) — conjugate transpose (m†, entered with (Key0[esc]) ct (Key0[esc]))

(RefLink[Tr, paclet:ref/Tr]) — trace

(RefLink[Det, paclet:ref/Det]) — determinant

(RefLink[Permanent, paclet:ref/Permanent]) — permanent

(RefLink[KroneckerProduct, paclet:ref/KroneckerProduct]) — matrix direct product (outer product)

(RefLink[MatrixPower, paclet:ref/MatrixPower]) — powers of numeric or symbolic matrices

(RefLink[MatrixExp, paclet:ref/MatrixExp])— matrix exponential

(RefLink[MatrixLog, paclet:ref/MatrixLog]) — matrix logarithm

(RefLink[MatrixFunction, paclet:ref/MatrixFunction]) — general matrix function

(RefLink[Eigenvalues, paclet:ref/Eigenvalues]), (RefLink[Eigenvectors, paclet:ref/Eigenvectors]) — exact or approximate eigenvalues and eigenvectors

(RefLink[Eigensystem, paclet:ref/Eigensystem]) — eigenvalues and eigenvectors together

(RefLink[CharacteristicPolynomial, paclet:ref/CharacteristicPolynomial]) — symbolic characteristic polynomial