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NDA Math Matrices
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© examsnet.com
Question : 22
Total: 69
If matrix
A
=
[
1
−
i
i
−
i
1
−
i
]
where
i
=
√
−
1
, then which of the following is correct?
[NDA-I 2020]
A
is hermitian
A
is skew-hermitian
(
A
)
T
+
A
is hermitian
(
A
)
T
+
A
is skew-hermitian
Validate
Solution:
👈: Video Solution
A square
M
matrix is said to be Hermitian (or self-adjoint) if it is equal to its. Own Hermitian conjugate, i.e.
(
M
)
T
=
M
Given Matrix
A
=
[
1
−
i
i
−
i
1
−
i
]
(
A
)
T
=
[
1
+
i
i
−
i
1
+
i
]
Now,
A
+
(
A
)
T
=
[
1
−
i
i
−
i
1
−
i
]
+
[
1
+
i
i
−
i
1
+
i
]
=
[
2
2
i
−
2
i
2
]
=
2
[
1
i
−
i
1
]
Conjugate transpose of
(
A
+
(
A
)
T
)
=
2
[
1
i
−
i
1
]
Hence,
(
A
)
T
+
A
is hermitian
© examsnet.com
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