Theorems · Definition · linear algebra

AlgEquiv.mapMatrix

{m : Type u_2} →
  {R : Type u_7} →
    {α : Type u_11} →
      {β : Type u_12} →
        [inst : Fintype m] →
          [inst_1 : DecidableEq m] →
            [inst_2 : CommSemiring R] →
              [inst_3 : Semiring α] →
                [inst_4 : Semiring β] →
                  [inst_5 : Algebra R α] → [inst_6 : Algebra R β] → (α ≃ₐ[R] β) → Matrix m m α ≃ₐ[R] Matrix m m β

The AlgEquiv between spaces of square matrices induced by an AlgEquiv between their coefficients. This is Matrix.map as an AlgEquiv.

Defined in

Mathlib.Data.Matrix.Basic

Cited by

9 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqCommSemiringSemiringSemiringAlgebraAlgebra