Linear maps between direct sums #
This file contains results about linear maps which respect direct sum decompositions of their domain and codomain.
If a linear map
f : M₁ → M₂ respects direct sum decompositions of
M₂, then it has a
block diagonal matrix with respect to bases compatible with the direct sum decompositions.
g are commuting endomorphisms of a finite, free
M, such that
is triangularizable, then to prove that the trace of
g ∘ f vanishes, it is sufficient to prove
that the trace of
g vanishes on each generalized eigenspace of