rightCancelEquiv_comp_rTensor_comp_symm

English

The identity T(n−2) = 2 X T(n−1) − T(n) holds for the Chebyshev polynomials for integer n.

Русский

Идентичность T(n−2) = 2 X T(n−1) − T(n) справедлива для целочисленного n.

LaTeX

$$T R (n-2) = 2 · X · T R (n-1) − T R n$$

Lean4

theorem rightCancelEquiv_comp_rTensor_comp_symm (f : P →ₗ[R] Q) :
    rightCancelEquiv Q e ∘ₗ (f.rTensor M).rTensor N ∘ₗ (rightCancelEquiv P e).symm = f := by
  rw [← LinearMap.comp_assoc, LinearEquiv.comp_toLinearMap_symm_eq]; ext; simp

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