# 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