Theorems · Theorem · linear algebra

basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix

∀ {ι : Type u_1} {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) (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 ι] [inst_8 : Fintype κ']
  [inst_9 : DecidableEq ι] [inst_10 : DecidableEq ι'],
  c.toMatrix ⇑c' * (LinearMap.toMatrix b' c') f * b'.toMatrix ⇑b = (LinearMap.toMatrix b c) f

Defined in

Mathlib.LinearAlgebra.Matrix.Basis

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleFintypeFiniteFintypeFintypeDecidableEqDecidableEq