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Kunze Linear Algebra
· Problem 8.1.1
Inner Product Spaces
Mathematics — Methods · inner-products
Problem
Let
V
V
V
be a vector space and
(
∣
)
(\ |\ )
(
∣
)
an inner product on
V
V
V
. (a) Show that
(
0
∣
β
)
=
0
(0|\beta) = 0
(
0∣
β
)
=
0
for all
β
\beta
β
in
V
V
V
. (b) Show that if
(
α
∣
β
)
=
0
(\alpha|\beta) = 0
(
α
∣
β
)
=
0
for all
β
\beta
β
in
V
V
V
, then
α
=
0
\alpha = 0
α
=
0
.
Related theory
Inner Products And Inner Product Spaces
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