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
KroneckerProduct — matrix direct product (outer product)
MatrixPower — powers of numeric or symbolic matrices
Eigenvalues,
Eigenvectors — exact or approximate eigenvalues and eigenvectors
Eigensystem — eigenvalues and eigenvectors together
CharacteristicPolynomial — symbolic characteristic polynomial
