Theorems · Theorem · linear algebra

TensorProduct.toMatrix_comm

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} {ι : Type u_7} {κ : Type u_8} [inst : DecidableEq ι]
  [inst_1 : DecidableEq κ] [inst_2 : Fintype ι] [inst_3 : Fintype κ] [inst_4 : CommRing R] [inst_5 : AddCommGroup M]
  [inst_6 : AddCommGroup N] [inst_7 : Module R M] [inst_8 : Module R N] (bM : Module.Basis ι R M)
  (bN : Module.Basis κ R N),
  (LinearMap.toMatrix (bM.tensorProduct bN) (bN.tensorProduct bM)) ↑(TensorProduct.comm R M N) =
    Matrix.submatrix 1 Prod.swap id

TensorProduct.comm corresponds to a permutation of the identity matrix.

Defined in: Mathlib.LinearAlgebra.TensorProduct.Matrix
Cited by: 0 results in Mathlib
Foundations: Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq DecidableEq Fintype Fintype CommRing AddCommGroup AddCommGroup Module Module

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