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Miklós Schweitzer
1957 Miklós Schweitzer
1
1
Part of
1957 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1957- Problem 1
Source:
10/16/2015
1. Let
C
i
j
C_{ij}
C
ij
(
i
,
j
=
1
,
2
,
3
i,j=1,2,3
i
,
j
=
1
,
2
,
3
) be the coefficients of a real non-involutive orthogonal transformation. Prove that the function
w
=
∑
i
,
j
=
1
3
c
i
j
z
i
z
j
ˉ
w= \sum_{i,j=1}^{3} c_{ ij}z_{i}\bar{z_{ j}}
w
=
∑
i
,
j
=
1
3
c
ij
z
i
z
j
ˉ
maps the surface of complex unit sphere
∑
i
=
1
3
z
i
z
i
ˉ
=
1
\sum_{i=1}^{3} z_{i}\bar{z_{i}} = 1
∑
i
=
1
3
z
i
z
i
ˉ
=
1
onto a triangle of the w-plane. (F. 3)
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