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2002 IMC
11
11
Part of
2002 IMC
Problems
(1)
IMC 2002 Problem 11
Source: IMC 2002 Day 2 Problem 5
10/27/2020
Let
A
A
A
be a complex
n
×
n
n \times n
n
×
n
Matrix for
n
>
1
n >1
n
>
1
. Let
A
H
A^{H}
A
H
be the conjugate transpose of
A
A
A
. Prove that
A
⋅
A
H
=
I
n
A\cdot A^{H} =I_{n}
A
⋅
A
H
=
I
n
if and only if
A
=
S
⋅
(
S
H
)
−
1
A=S\cdot (S^{H})^{-1}
A
=
S
⋅
(
S
H
)
−
1
for some complex Matrix
S
S
S
.
linear algebra
matrix
complex numbers