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Putnam
2005 Putnam
A4
A4
Part of
2005 Putnam
Problems
(1)
Putnam 2005 A4
Source:
12/5/2005
Let
H
H
H
be an
n
×
n
n\times n
n
×
n
matrix all of whose entries are
±
1
\pm1
±
1
and whose rows are mutually orthogonal. Suppose
H
H
H
has an
a
×
b
a\times b
a
×
b
submatrix whose entries are all
1.
1.
1.
Show that
a
b
≤
n
.
ab\le n.
ab
≤
n
.
Putnam
linear algebra
matrix
inequalities
vector
ratio
absolute value