Theorems · Theorem · linear algebra

basis_toMatrix_mul

∀ {ι : Type u_1} {ι' : Type u_2} {κ : Type u_3} {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]
  [inst_5 : Fintype ι'] [inst_6 : Fintype κ] [inst_7 : Finite ι] [inst_8 : DecidableEq κ] (b₁ : Module.Basis ι R M)
  (b₂ : Module.Basis ι' R M) (b₃ : Module.Basis κ R N) (A : Matrix ι' κ R),
  b₁.toMatrix ⇑b₂ * A = (LinearMap.toMatrix b₃ b₁) ((Matrix.toLin b₃ b₂) A)

Defined in

Mathlib.LinearAlgebra.Matrix.Basis

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleFintypeFintypeFiniteDecidableEq