Commit 2025-07-27 15:47 0a739db8
View on Github →feat(LinearAlgebra/Projection): lemmas on projections and invariant submodules (#25874)
Proving some lemmas on invariant submodules, such as:
For idempotent f
and any operator T
:
range f
is invariant underT
ifff ∘ T ∘ f = T ∘ f
ker f
is invariant underT
ifff ∘ T ∘ f = f ∘ T
f
andT
commute iff bothrange f
andker f
are invariant underT
Added for both linear maps and continuous linear maps for convenience. Taken from leanprover-community/mathlib3#18289.