# Complex conjugate of a 5 x 5 matrices?

• ayalam
In summary, to get the complex conjugate of a matrix, you simply conjugate each entry. To find the Hermitian conjugate or adjoint, you take the complex conjugate of each entry and then transpose the matrix. A 5*5 matrix example was provided to demonstrate this process. It is important to differentiate between the transpose and Hermitian conjugate, as they are not the same.
ayalam
How do you do it?

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

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

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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.

Can i get a 5*5 matrices example

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

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

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

nice examples

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## 1. What is a complex conjugate of a 5 x 5 matrix?

The complex conjugate of a 5 x 5 matrix is a matrix with the same elements, but with the imaginary components of each element changed to their negative value.

## 2. How is the complex conjugate of a 5 x 5 matrix calculated?

The complex conjugate of a 5 x 5 matrix is calculated by taking the complex conjugate of each individual element in the matrix.

## 3. What is the purpose of finding the complex conjugate of a 5 x 5 matrix?

Finding the complex conjugate of a 5 x 5 matrix is useful in various mathematical operations, particularly in solving equations involving complex numbers.

## 4. Can a complex conjugate of a 5 x 5 matrix be a real matrix?

No, a complex conjugate of a 5 x 5 matrix will always contain complex numbers and cannot be a real matrix.

## 5. Is the complex conjugate of a 5 x 5 matrix unique?

Yes, the complex conjugate of a 5 x 5 matrix is unique and will always have the same elements in the same order as the original matrix.

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