Theorems · Definition · functional analysis

LinearMap.toMatrixOrthonormal

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : InnerProductSpace 𝕜 E] →
          {n : Type u_6} →
            [inst_3 : Fintype n] →
              [DecidableEq n] →
                [inst_5 : FiniteDimensional 𝕜 E] → OrthonormalBasis n 𝕜 E → (E →ₗ[𝕜] E) ≃⋆ₐ[𝕜] Matrix n n 𝕜

The star algebra equivalence between the linear endomorphisms of finite-dimensional inner product space and square matrices induced by the choice of an orthonormal basis.

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

4 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeDecidableEqFiniteDimensional