Complex conjugate of a 5 x 5 matrices?

1. Jun 2, 2005

ayalam

How do you do it?

2. Jun 3, 2005

matt grime

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

3. Jun 6, 2005

qqchico

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

Last edited: Jun 6, 2005
4. Jun 6, 2005

HallsofIvy

Staff Emeritus
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.

5. Jun 6, 2005

qqchico

Can i get a 5*5 matrices example

6. Jun 7, 2005

Nylex

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

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

7. Jun 7, 2005

HallsofIvy

Staff Emeritus
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
$$A^* = \left(\begin{array}{ccccc}0 & -i & 3 & 2 & 1 + 2i \\ i & 7 & 6 & 4 & 0 \\3 - i & 2 & 0 & 2i & 4 \\ 9 & 1 & -i & 8 & 1 \\ 0 & 0 & 0 & -7i & 0\end{array}\right)$$

8. Jun 10, 2005

qqchico

nice examples

Last edited: Jun 10, 2005