Theorems · Theorem · linear algebra

Module.Basis.linearMap_apply_apply

∀ {R : Type u_1} {M₁ : Type u_3} {M₂ : Type u_4} {ι₁ : Type u_6} {ι₂ : Type u_7} [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M₁] [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M₁] [inst_4 : Module R M₂]
  [inst_5 : Fintype ι₁] [inst_6 : Fintype ι₂] [inst_7 : DecidableEq ι₁] (b₁ : Module.Basis ι₁ R M₁)
  (b₂ : Module.Basis ι₂ R M₂) (ij : ι₂ × ι₁) (k : ι₁), ((b₁.linearMap b₂) ij) (b₁ k) = if ij.2 = k then b₂ ij.1 else 0

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleFintypeFintypeDecidableEq