Complex conjugate of a 5 x 5 matrices?

[ayalam]

How do you do it?

 

[matt grime]

To get the complex conjugate of any matrix you just conjugate each entry.

 

[qqchico]

Sorry I am doing something similar; converting a ket into a bra. wouldn't something change like order.

 

[HallsofIvy]

matt grime is completely right for "complex conjugate". However, you may be intending "Hermitian conjugate" or "adjoint". To find the Hermitian conjugate (adjoint) of a complex matrix you take the complex conjugate of each entry and take the transpose: rows become columns.

 

[qqchico]

Can i get a 5*5 matrices example

 

[Nylex]

A = \left(\begin{array}{ccccc}0 &amp; i &amp; 3 &amp; 2 &amp; 1 - 2i \\ -i &amp; 7 &amp; 6 &amp; 4 &amp; 0 \\<br /> 3 + i &amp; 2 &amp; 0 &amp; -2i &amp; 4 \\ 9 &amp; 1 &amp; i &amp; 8 &amp; 1 \\ 0 &amp; 0 &amp; 0 &amp; 7i &amp; 0\end{array}\right) A^T = \left(\begin{array}{ccccc}0 &amp; -i &amp; 3 + i &amp; 9 &amp; 0 \\ i &amp; 7 &amp; 2 &amp; 1 &amp; 0 \\ 3 &amp; 6 &amp; 0 &amp; i &amp; 0 \\ 2 &amp; 4 &amp; -2i &amp; 8 &amp; 7i \\ 1 - 2i &amp; 0 &amp; 4 &amp; 1 &amp; 0\end{array}\right) A^\dagger = \left(\begin{array}{ccccc}0 &amp; i &amp; 3 - i &amp; 9 &amp; 0 \\ -i &amp; 7 &amp; 2 &amp; 1 &amp; 0 \\ 3 &amp; 6 &amp; 0 &amp; -i &amp; 0 \\ 2 &amp; 4 &amp; 2i &amp; 8 &amp; -7i \\ 1 + 2i &amp; 0 &amp; 4 &amp; 1 &amp; 0\end{array}\right)

I hope that's right and I've not made any mistakes.

 

[HallsofIvy]

In Nylex's example, A^T is the transpose and A^{\dagger} is the Hermitian conjugate or adjoint.
Using the same example, the "complex conjugate" that was originally asked for, and matt grimes described, would be
A^* = \left(\begin{array}{ccccc}0 &amp; -i &amp; 3 &amp; 2 &amp; 1 + 2i \\ i &amp; 7 &amp; 6 &amp; 4 &amp; 0 \\3 - i &amp; 2 &amp; 0 &amp; 2i &amp; 4 \\ 9 &amp; 1 &amp; -i &amp; 8 &amp; 1 \\ 0 &amp; 0 &amp; 0 &amp; -7i &amp; 0\end{array}\right)

 

[qqchico]

nice examples