comp — Mathlib

English

For a finite basis b, B.flip.dualSubmodule (B.dualSubmodule (span_R(range b))) = span_R(range b).

Русский

Для базиса b: B.flip.dualSubmodule(B.dualSubmodule(span_R(range b))) = span_R(range b).

LaTeX

$$$$ B.flip.dualSubmodule( B.dualSubmodule(\mathrm{span}_R(\mathrm{range}\, b)) ) = \mathrm{span}_R(\mathrm{range}\, b). $$$$

Lean4

/-- Apply a linear map on the left and right argument of a bilinear form. -/
def comp (B : BilinForm R M') (l r : M →ₗ[R] M') : BilinForm R M :=
  B.compl₁₂ l r

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