Theorems · Theorem · linear algebra

LinearMap.BilinForm.dualBasis_eq_iff

∀ {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 : Module.Basis ι K V) (v : ι → V), ⇑(B.dualBasis hB b) = v ↔ ∀ (i j : ι), (B (v i)) (b j) = if j = i 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