These constructions have special mathematical properties:

<box-matrix> ( r -- matrix )

<hankel-matrix> ( n -- matrix )

<hilbert-matrix> ( m n -- matrix )

<toeplitz-matrix> ( n -- matrix )

<vandermonde-matrix> ( u n -- matrix )

Common transformation matrices:

<frustum-matrix4> ( xy-dim near far -- matrix )

<ortho-matrix4> ( factors -- matrix )

<rotation-matrix3> ( axis theta -- matrix )

<rotation-matrix4> ( axis theta -- matrix )

<scale-matrix3> ( factors -- matrix )

<scale-matrix4> ( factors -- matrix )

<skew-matrix4> ( theta -- matrix )

<translation-matrix4> ( offset -- matrix )

<random-integer-matrix> ( m n max -- matrix )

<random-unit-matrix> ( m n max -- matrix )

invertible-matrix? ( matrix -- ? )

linearly-independent-matrix? ( matrix -- ? )

Common algorithms on matrices:

gram-schmidt ( matrix -- orthogonal )

gram-schmidt-normalize ( matrix -- orthonormal )

kronecker-product ( m1 m2 -- m )

outer-product ( u v -- matrix )

Matrix algebra:

rank ( matrix -- rank )

nullity ( matrix -- nullity )

determinant ( matrix -- determinant )

1/det ( matrix -- 1/det )

m*1/det ( matrix -- matrix' )

>minors ( matrix -- matrix' )

>cofactors ( matrix -- matrix' )

multiplicative-inverse ( x -- y )

Covariance in matrices:

covariance-matrix ( matrix -- cov )

covariance-matrix-ddof ( matrix ddof -- cov )

sample-covariance-matrix ( matrix -- cov )

Errors thrown by this vocabulary:

negative-power-matrix ( m n -- * )

non-square-determinant ( m n -- * )

undefined-inverse ( m n r -- * )