Theorems · Theorem · linear algebra

LinearPMap.supSpanSingleton_apply_mk

∀ {E : Type u_4} [inst : AddCommGroup E] {F : Type u_5} [inst_1 : AddCommGroup F] {K : Type u_7} {L : Type u_8}
  [inst_2 : DivisionRing K] [inst_3 : DivisionRing L] {σ : K →+* L} [inst_4 : Module K E] [inst_5 : Module L F]
  (f : E →ₛₗ.[σ] F) (x : E) (y : F) (hx : x ∉ f.domain) (x' : E) (hx' : x' ∈ f.domain) (c : K),
  ↑(f.supSpanSingleton x y hx) ⟨x' + c • x, ⋯⟩ = ↑f ⟨x', hx'⟩ + σ c • y

Defined in

Mathlib.LinearAlgebra.LinearPMap

Cited by

5 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupDivisionRingDivisionRingModuleModule