Theorems · Theorem · linear algebra

mul_basis_toMatrix

∀ {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 : Finite κ] [inst_7 : Fintype ι] [inst_8 : DecidableEq ι] [inst_9 : DecidableEq ι']
  (b₁ : Module.Basis ι R M) (b₂ : Module.Basis ι' R M) (b₃ : Module.Basis κ R N) (A : Matrix κ ι R),
  A * b₁.toMatrix ⇑b₂ = (LinearMap.toMatrix b₂ b₃) ((Matrix.toLin b₁ b₃) A)

Defined in

Mathlib.LinearAlgebra.Matrix.Basis

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleFintypeFiniteFintypeDecidableEqDecidableEq