Theorems · Theorem · linear algebra

LinearMap.rank_add_le

∀ {K : Type u} {V : Type v} {V' : Type v'} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [inst_3 : AddCommGroup V'] [inst_4 : Module K V'] (f g : V →ₗ[K] V'), (f + g).rank ≤ f.rank + g.rank

Defined in

Mathlib.LinearAlgebra.Dimension.LinearMap

Cited by

1 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddCommGroupModule