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16.-Linear-Algebra-by-Kenneth-Hoffman
· Problem 8.2.5
Inner Product Spaces
Mathematics — Linear Algebra · inner-products
Problem
Let
V
V
V
be an inner product space, and let
α
\alpha
α
,
β
\beta
β
be vectors in
V
V
V
. Show that
α
=
β
\alpha = \beta
α
=
β
if and only if
(
α
∣
γ
)
=
(
β
∣
γ
)
(\alpha|\gamma) = (\beta|\gamma)
(
α
∣
γ
)
=
(
β
∣
γ
)
for every
γ
\gamma
γ
in
V
V
V
.
Related theory
Inner Products And Inner Product Spaces
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