Theorems · Theorem · linear algebra

LinearMap.BilinForm.apply_dualBasis_right

∀ {V : Type u_5} {K : Type u_6} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Type u_9}
  [inst_3 : DecidableEq ι] [inst_4 : Finite ι] {B : LinearMap.BilinForm K V} (hB : B.Nondegenerate),
  B.IsSymm → ∀ (b : Module.Basis ι K V) (i j : ι), (B (b i)) ((B.dualBasis hB b) j) = if i = j then 1 else 0

Defined in

Mathlib.LinearAlgebra.BilinearForm.Properties

Cited by

1 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleDecidableEqFinite