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Vojtěch Jarník IMC
2007 VJIMC
Problem 2
A+A^T=I implies det A>0
A+A^T=I implies det A>0
Source: VJIMC 2007 2.2
June 24, 2021
matrix
linear algebra
Problem Statement
Let
A
A
A
be a real
n
×
n
n\times n
n
×
n
matrix satisfying
A
+
A
T
=
I
,
A+A^{\text T}=I,
A
+
A
T
=
I
,
where
A
T
A^{\text T}
A
T
denotes the transpose of
A
A
A
and
I
I
I
the
n
×
n
n\times n
n
×
n
identity matrix. Show that
det
A
>
0
\det A>0
det
A
>
0
.
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