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(1)
Matrix equals its conjugate transpose
Source: 17th SEEMOUS 2023, Problem 3
3/9/2023
Prove that if
A
A{}
A
is an
n
×
n
n\times n
n
×
n
matrix with complex entries such that
A
+
A
∗
=
A
2
A
∗
A+A^*=A^2A^*
A
+
A
∗
=
A
2
A
∗
then
A
=
A
∗
A=A^*
A
=
A
∗
. (Here, we denote by
M
∗
M^*
M
∗
the conjugate transpose
M
‾
t
\overline{M}^t
M
t
of the matrix
M
M{}
M
).
linear algebra
matrix
Seemous