Smile provides functions for doing linear algebra on matrices and for solving a system of linear equations.

addlist, sublist, multlist, divlist

The four elementary arithmetic operators, that you can apply to 1d arrays as well as to matrices. The computation occurs element by element: multlist is not the product of matrices in the usual sense.

transpose

Returns the transposed matrix ^tM of the argument. If you pass a list of two matrices of the same size, transpose understands that it as a complex matrix {real part, imaginary part}.

multmatrix

The product of matrices A x B, or the product of a matrix by a vector M x v, of the scalar product of two vectors <v₁,v₂>.

invertmatrix

Returns the inverse matrix M^-1 of the argument.

solve linear system

Being given A and B, finds the solution X of the system A.X = B. B should be an array of real (a vector).

compute eigenvalues

Returns the eigenvalues and eigenvectors of a matrix.

LUdecomposition

Performs the LU decomposition of a matrix A (A = P.L.U), or a Chowlesky decomposition (A = U**TU) for a positive matrix.

pivot

Applies a permutation (for instance, such as returned by LUdecomposition) to a matrix ot to a array of real (a vector).

compute determinant

Returns the determinant of a matrix.