Theorems · Definition · linear algebra

LinearMap.BilinForm.toMatrix

{R₁ : Type u_1} →
  {M₁ : Type u_2} →
    [inst : CommSemiring R₁] →
      [inst_1 : AddCommMonoid M₁] →
        [inst_2 : Module R₁ M₁] →
          {n : Type u_5} →
            [Fintype n] → [DecidableEq n] → Module.Basis n R₁ M₁ → LinearMap.BilinForm R₁ M₁ ≃ₗ[R₁] Matrix n n R₁

BilinForm.toMatrix b is the equivalence between R-bilinear forms on M and n-by-n matrices with entries in R, if b is an R-basis for M.

Defined in

Mathlib.LinearAlgebra.Matrix.BilinearForm

Cited by

47 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleFintypeDecidableEq