Theorems · Definition · linear algebra

Matrix.kroneckerStarAlgEquiv

(m : Type u_2) →
  (n : Type u_3) →
    (R : Type u_5) →
      [inst : CommSemiring R] →
        [inst_1 : Fintype n] →
          [inst_2 : DecidableEq n] →
            [inst_3 : Fintype m] →
              [inst_4 : DecidableEq m] →
                [inst_5 : StarRing R] → TensorProduct R (Matrix m m R) (Matrix n n R) ≃⋆ₐ[R] Matrix (m × n) (m × n) R

Matrix.kronecker as a ⋆-algebra equivalence, when the two arguments are tensored.

Defined in

Mathlib.RingTheory.MatrixAlgebra

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommSemiringFintypeDecidableEqFintypeDecidableEqStarRing