This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Matrix Operations
Mathematica's matrix operations handle both numeric and symbolic matrices, automatically accessing large numbers of highly efficient algorithms. Mathematica 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 Esc tr Esc)
ConjugateTranspose conjugate transpose (, entered with Esc ct Esc)
Tr trace
Det determinant
KroneckerProduct matrix direct product (outer product)

MatrixPower powers of numeric or symbolic matrices
MatrixExp matrix exponential

Eigenvalues, Eigenvectors exact or approximate eigenvalues and eigenvectors
Eigensystem eigenvalues and eigenvectors together
CharacteristicPolynomial symbolic characteristic polynomial
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