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.

+, *, ^, ... all automatically work element-wise

Dot (.) products of matrices, automatically handling row and column vectors

Inverse matrix inverse (use LinearSolve for linear systems)

Transpose transpose (, entered with tr)

ConjugateTranspose conjugate transpose (, entered with ct)

Tr trace

Det determinant

Adjugate adjugate

Permanent permanent

KroneckerProduct matrix direct product (outer product)

MatrixPower powers of numeric or symbolic matrices

MatrixExp matrix exponential

MatrixLog matrix logarithm

MatrixFunction general matrix function

Eigenvalues, Eigenvectors exact or approximate eigenvalues and eigenvectors

Eigensystem eigenvalues and eigenvectors together

CharacteristicPolynomial symbolic characteristic polynomial