toMatrix_orthonormalBasis_mem_orthogonal

English

The relation between basisFun and toBasis is identity up to a simple isomorphism.

Русский

Связь basisFun и toBasis выражается тождественно через простую изоморфность.

LaTeX

$$$$ (EuclideanSpace.basisFun ι 𝕜).toBasis = PiLp.basisFun 2 𝕜 ι. $$$$

Lean4

/-- The change-of-basis matrix between two orthonormal bases `a`, `b` is an orthogonal matrix. -/
theorem toMatrix_orthonormalBasis_mem_orthogonal : a.toBasis.toMatrix b ∈ Matrix.orthogonalGroup ι ℝ :=
  a.toMatrix_orthonormalBasis_mem_unitary b

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