A = ⎡ ⎢ ⎣ 1 2 − 3 i 3 + 4 i 2 + 3 i 0 4

Question

A
=



1
2

3
i
3
+
4
i
2
+
3
i
0
4

5
i
3

4
i
4
+
5
i
2



A=[12−3i3+4i2+3i04−5i3−4i4+5i2]
then A is

      
symmetric matrix

      
skew – symmetric matrix

      
hermitian matrix

      
skew-hermitian matrix​

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Cora 3 weeks 2021-11-07T10:37:05+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-07T10:38:45+00:00

    Step-by-step explanation:

    Given that:

    \left[\begin{array}{ccc}1&2-3i&3+4i\\2+3i&0&4-5i\\3-4i&4+5i&2\end{array}\right]

    To find:

    A is

    a) symmetric matrix

    b) skew – symmetric matrix

    c) hermitian matrix

    d) skew-hermitian matrix

    Solution:

    A matrix is called hermitian matrix,if transpose of A and it’s conjugate is equal to matrix itself.

    A=\left[\begin{array}{ccc}1&2-3i&3+4i\\2+3i&0&4-5i\\3-4i&4+5i&2\end{array}\right]...eq1

    A^T=\left[\begin{array}{ccc}1&2+3i&3-4i\\2-3i&0&4+5i\\3+4i&4-5i&2\end{array}\right]

    Take conjugate of Complex numbers

    if

    z = a + ib \\

    then its conjugate is

     z' = a - ib \\

    A^{TC}=\left[\begin{array}{ccc}1&2-3i&3+4i\\2+3i&0&4-5i\\3-4i&4+5i&2\end{array}\right]...eq2

    From eq1 and eq2

    it is clear that

    A=A^{TC}

    Thus,

    Matrix A is Hermitian matrix.

    Option C is correct.

    Hope it helps you.

    0
    2021-11-07T10:39:01+00:00

    Answer:

    Matrix A is Hermitian matrix.

    Matrix A is Hermitian matrix.Option C is correct.

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