Some of the linear algebra commands are
DiagonalMatrix, Matrix,
LowerTriangularMatrix, Submatrix,
SwapRows, AddColumn,
MultiplyRow, Nullspace,
Determinant, CharacteristicPolynomial,
Trace, Eigenvalues,
MinimalPolynomial, Eigenspace,
Rank, JordanForm,
SmithForm, ElementaryDivisors,
and lots of others.