Theorems · Theorem · linear algebra

setBasisOfTopLeSpanOfCardEqFinrank_repr_apply

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : OrzechProperty R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] {s : Set M} [inst_4 : Fintype ↑s] (le_span : ⊤ ≤ Submodule.span R s)
  (card_eq : s.toFinset.card = Module.finrank R M) (x : M),
  (setBasisOfTopLeSpanOfCardEqFinrank le_span card_eq).repr x =
    ⋯.repr ((LinearMap.codRestrict (Submodule.span R (Set.range Subtype.val)) LinearMap.id ⋯) x)

Defined in

Mathlib.LinearAlgebra.Dimension.OrzechProperty

Cited by

0 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringOrzechPropertyAddCommMonoidModuleFintype