mathlib documentation

linear_algebra.quadratic_form.real

Real quadratic forms #

Sylvester's law of inertia equivalent_one_neg_one_weighted_sum_squared: A real quadratic form is equivalent to a weighted sum of squares with the weights being ±1 or 0.

When the real quadratic form is nondegerate we can take the weights to be ±1, as in equivalent_one_zero_neg_one_weighted_sum_squared.

The isometry between a weighted sum of squares with weights u on the (non-zero) real numbers and the weighted sum of squares with weights sign ∘ u.

Equations

Sylvester's law of inertia: A nondegenerate real quadratic form is equivalent to a weighted sum of squares with the weights being ±1.

Sylvester's law of inertia: A real quadratic form is equivalent to a weighted sum of squares with the weights being ±1 or 0.