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Gauss-Lagrange Algorithm for Real Quadratic Forms
Author

Gabriel Chenevert
Organization: Université de Montreal
Old MathSource #

0210-250
Revision date

1999-07-15
Description

This package implements the Gauss-Lagrange algorithm to find the canonical form under congruence of a symmetric matrix associated with a real quadratic form. This allows one to classify all real quadratic forms, and in particular to determine whether a given quadratic form is positive definite or not. The package also implements elementary row and column operations on any matrix. Examples and explanations are found in the notebook GaussLagrange.nb.
Subject

*Mathematics > Algebra > Linear Algebra
Keywords

Gauss-Lagrange algorithm, real quadratic form, canonical form of a symmetric matrix under congruence, definiteness
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GaussLagrange.m (5.5 KB) - Mathematica package
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GaussLagrange.nb (21.9 KB) - Explanatory Mathematica notebook