Kunze Linear Algebra · Problem 6.7.1

Elementary Canonical Forms

Mathematics — Methods · projection-invariance-range-nullspace

Problem

Let

E

be a projection of

V

and let

T

be a linear operator on

V

. Prove that the range of

E

is invariant under

T

if and only if

ETE = TE

. Prove that both the range and null space of

E

are invariant under

T

if and only if

ET = TE