Bilinear form

This file defines a bilinear form over a module. Basic ideas such as orthogonality are also introduced, as well as reflexivive, symmetric and alternating bilinear forms.

A bilinear form on an R-module V, is a function from V x V to R, that is linear in both arguments

Notations

Given any term B of type bilin_form, due to a coercion, can use the notation B x y to refer to the function field, ie. B x y = B.bilin x y.

References

Tags

Bilinear form,


bilin_form

A bilinear form over a module

bilin_form.is_ortho

The proposition that two elements of a bilinear form space are orthogonal

refl_bilin_form.is_refl

The proposition that a bilinear form is reflexive

sym_bilin_form.is_sym

The proposition that a bilinear form is symmetric

alt_bilin_form.is_alt

The proposition that a bilinear form is alternating