Theorems · Theorem · linear algebra

LinearMap.BilinForm.linearIndependent_of_iIsOrtho

∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {n : Type w}
  {B : LinearMap.BilinForm K V} {v : n → V}, B.iIsOrtho v → (∀ (i : n), (B (v i)) (v i) ≠ 0) → LinearIndependent K v

A set of orthogonal vectors v with respect to some bilinear form B is linearly independent if for all i, B (v i) (v i) ≠ 0.

Defined in

Mathlib.LinearAlgebra.BilinearForm.Orthogonal

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModule