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Kunze Linear Algebra
· Problem 8.3.11
Inner Product Spaces
Mathematics — Methods · self-adjoint-idempotent
Problem
Let
V
V
V
be a finite-dimensional inner product space, and let
E
E
E
be an idempotent linear operator on
V
V
V
, i.e.,
E
2
=
E
E^2 = E
E
2
=
E
. Prove that
E
E
E
is self-adjoint if and only if
E
E
∗
=
E
∗
E
EE^* = E^*E
E
E
∗
=
E
∗
E
.
Related theory
Adjoint Functors And Freyd S Adjoint Functor Theorem
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