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Kunze Linear Algebra
· Problem 8.3.12
Inner Product Spaces
Mathematics — Methods · self-adjoint-operators
Problem
Let
V
V
V
be a finite-dimensional complex inner product space, and let
T
T
T
be a linear operator on
V
V
V
. Prove that
T
T
T
is self-adjoint if and only if
(
T
α
∣
α
)
(T\alpha|\alpha)
(
T
α
∣
α
)
is real for every
α
\alpha
α
in
V
V
V
.
Related theory
self-adjoint-operators
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