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Kunze Linear Algebra
· Problem 10.4.3
Bilinear Forms
Mathematics — Methods · orthogonal-group-sum-squares
Problem
Let
y
j
=
∑
k
=
1
n
M
j
k
x
k
y_j = \sum_{k=1}^n M_{jk} x_k
y
j
=
k
=
1
∑
n
M
j
k
x
k
where
M
M
M
is a member of
O
(
n
,
C
)
O(n, C)
O
(
n
,
C
)
. Show that
∑
j
y
j
2
=
∑
j
x
j
2
.
\sum_j y_j^2 = \sum_j x_j^2.
j
∑
y
j
2
=
j
∑
x
j
2
.
Related theory
Group Frequencies And Functional Group Identification
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