Theorems · Theorem · linear algebra

Matrix.toLin_transpose

∀ {K : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {ι₁ : Type u_4} {ι₂ : Type u_5} [inst : CommSemiring K]
  [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁] [inst_3 : AddCommGroup V₂] [inst_4 : Module K V₂]
  [inst_5 : Fintype ι₁] [inst_6 : Fintype ι₂] [inst_7 : DecidableEq ι₁] [inst_8 : DecidableEq ι₂]
  {B₁ : Module.Basis ι₁ K V₁} {B₂ : Module.Basis ι₂ K V₂} (M : Matrix ι₁ ι₂ K),
  (Matrix.toLin B₁.dualBasis B₂.dualBasis) M.transpose = Module.Dual.transpose ((Matrix.toLin B₂ B₁) M)

Defined in

Mathlib.LinearAlgebra.Matrix.Dual

Cited by

1 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommGroupModuleAddCommGroupModuleFintypeFintypeDecidableEqDecidableEq