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Kunze Linear Algebra
· Problem 8.2.12
Inner Product Spaces
Mathematics — Methods · orthogonal-projection
Problem
Let
W
W
W
be a finite-dimensional subspace of an inner product space
V
V
V
, and let
E
E
E
be the orthogonal projection of
V
V
V
on
W
W
W
. Prove that
(
E
α
∣
β
)
=
(
α
∣
E
β
)
(E\alpha|\beta) = (\alpha|E\beta)
(
E
α
∣
β
)
=
(
α
∣
E
β
)
for all
α
\alpha
α
,
β
\beta
β
in
V
V
V
.
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