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Miklós Schweitzer
2012 Miklós Schweitzer
5
5
Part of
2012 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 2012 P5
Source: Miklós Schweitzer 2012 P5
8/20/2018
Let
V
1
,
V
2
,
V
3
,
V
4
V_1,V_2,V_3,V_4
V
1
,
V
2
,
V
3
,
V
4
be four dimensional linear subspaces in
R
8
\mathbb{R}^8
R
8
such that the intersection of any two contains only the zero vector. Prove that there exists a linear four dimensional subspace
W
W
W
in
R
8
\mathbb{R}^8
R
8
such that all four vector spaces
W
∩
V
i
W\cap V_i
W
∩
V
i
are two dimensional.
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