Smith normal form basis

Let A be a non-zero m×n matrix over a principal ideal domain (PID). Then, there exist invertible m×m and n×n matrices S and T, so that

S·A·T = α10000α200000αr000

where the diagonal elements satisfy αi|αi+1. They are called invariant factors.

Syntax

smith_normal_form_basis(Matrix)

Description

Given a matrix, returns a list: the first element is matrix SLaTeXS, the second element is the diagonal matrix and the third element is TLaTeXT.

linear_algebra.smith_normal_form_basis.calc.png