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Determinant

Det[{{1, 2, 1}, {1, 1, 0}, {0, 1, 1}}]

Cross Product

Cross[{1, 2, 3}, {3, 4, 5}]

Matrix Product

{{1, 2}, {3, 4}} . {{-1, 1}, {0, 2}}

Row Reduction

Matrix Rank

Eigenvalues

Eigenvalues[{{3, -1}, {0, 2}}]

Eigenvectors

Eigenvectors[{{-2, 5, 7}, {3, 11, 15}, {-4, -3, 10}}]

Jordan Decomposition

JordanDecomposition[{{-1, 5}, {-3, 11}}]

Kernel

Null Space

NullSpace[{{1, 3, 3}, {-3, -5, -3}, {3, 3, 0}}]

Positive Definite

PositiveDefiniteMatrixQ[{{3, -3}, {-3, 5}}]

Probability

Distributions

Wolfram Alpha Reference

NormalDistribution[\[Mu], \[Sigma]]