Let { u 1 , . . . , u n } be an orthonormal basis for a complex inner product space V, and let z = a 1 u 1 + a 2 u 2 + ⋯ + a n u n w = b 1 u 1 + b 2 u 2 + ⋯ + b n u n Show that 〈 z , w 〉 = ∑ i = 1 n b i ¯ a i
Let { u 1 , . . . , u n } be an orthonormal basis for a complex inner product space V, and let z = a 1 u 1 + a 2 u 2 + ⋯ + a n u n w = b 1 u 1 + b 2 u 2 + ⋯ + b n u n Show that 〈 z , w 〉 = ∑ i = 1 n b i ¯ a i
Solution Summary: The author explains that the orthogonal basis for complex inner product space V is leftu_1,mathrm....
Let
{
u
1
,
.
.
.
,
u
n
}
be an orthonormal basis for a complex inner product space V, and let
z
=
a
1
u
1
+
a
2
u
2
+
⋯
+
a
n
u
n
w
=
b
1
u
1
+
b
2
u
2
+
⋯
+
b
n
u
n
Show that
〈
z
,
w
〉
=
∑
i
=
1
n
b
i
¯
a
i
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