Theorems · Definition · linear algebra

matrixEquivTensor

(n : Type u_3) →
  (R : Type u_5) →
    (A : Type u_7) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] →
            [inst_3 : Fintype n] → [inst_4 : DecidableEq n] → Matrix n n A ≃ₐ[R] TensorProduct R A (Matrix n n R)

The R-algebra isomorphism Matrix n n A ≃ₐ[R] (A ⊗[R] Matrix n n R).

Defined in

Mathlib.RingTheory.MatrixAlgebra

Cited by

5 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraFintypeDecidableEq