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
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