Theorems · Theorem · linear algebra

basis_toMatrix_mul_linearMap_toMatrix

∀ {ι' : Type u_2} {κ : Type u_3} {κ' : Type u_4} {R : Type u_5} {M : Type u_6} [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Type u_9} [inst_3 : AddCommMonoid N] [inst_4 : Module R N]
  (b' : Module.Basis ι' R M) (c : Module.Basis κ R N) (c' : Module.Basis κ' R N) (f : M →ₗ[R] N) [inst_5 : Fintype ι']
  [inst_6 : Finite κ] [inst_7 : Fintype κ'] [inst_8 : DecidableEq ι'],
  c.toMatrix ⇑c' * (LinearMap.toMatrix b' c') f = (LinearMap.toMatrix b' c) f

Defined in

Mathlib.LinearAlgebra.Matrix.Basis

Cited by

3 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleFintypeFiniteFintypeDecidableEq