toMvPolynomial — Mathlib

English

Similarly, an endomorphism f on M commutes with the identity map: f ∘ id = id ∘ f.

Русский

Аналогично, эндоморфизм f на M коммутирует с тождественным отображением: f ∘ id = id ∘ f.

LaTeX

$$Commute$f, LinearMap.id$$$

Lean4

/-- Let `M` be an `(m × n)`-matrix over `R`.
Then `Matrix.toMvPolynomial M` is the family (indexed by `i : m`)
of multivariate polynomials in `n` variables over `R` that evaluates on `c : n → R`
to the dot product of the `i`-th row of `M` with `c`:
`Matrix.toMvPolynomial M i` is the sum of the monomials `C (M i j) * X j`. -/
noncomputable def toMvPolynomial (M : Matrix m n R) (i : m) : MvPolynomial n R :=
  ∑ j, monomial (.single j 1) (M i j)

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