Theorems · Theorem · linear algebra

Matrix.kroneckerTMulStarAlgEquiv_symm_apply

∀ {m : Type u_2} {n : Type u_3} (R : Type u_5) (S : Type u_6) {A : Type u_7} {B : Type u_8} [inst : CommSemiring R]
  [inst_1 : Semiring A] [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : Fintype n]
  [inst_6 : DecidableEq n] [inst_7 : CommSemiring S] [inst_8 : Algebra R S] [inst_9 : Algebra S A]
  [inst_10 : IsScalarTower R S A] [inst_11 : Fintype m] [inst_12 : DecidableEq m] [inst_13 : StarRing R]
  [inst_14 : StarAddMonoid A] [inst_15 : StarAddMonoid B] [inst_16 : StarModule R A] [inst_17 : StarModule R B]
  (x : Matrix (m × n) (m × n) (TensorProduct R A B)),
  (Matrix.kroneckerTMulStarAlgEquiv m n R S A B).symm x = (kroneckerTMulLinearEquiv m m n n R S A B).symm x

Defined in

Mathlib.RingTheory.MatrixAlgebra

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraFintypeDecidableEqCommSemiringAlgebraAlgebraIsScalarTowerFintypeDecidableEqStarRingStarAddMonoidStarAddMonoidStarModuleStarModule