- #1

- 878

- 224

I have a 2x2 hermitian matrix like:

$$

A = \begin{bmatrix}

a && b \\

-b && -a

\end{bmatrix}

$$

(b is imaginary to ensure that it is hermitian). I would like to find an orthogonal transformation M that makes A skew-symmetric:

$$

\hat A = \begin{bmatrix}

0 && c \\

-c && 0

\end{bmatrix}

$$

Is it possible, or I need to constrain my problem more? I need M to be orthogonal and with det(M) = 1. I was thinking maybe there are some tricks involving Pauli matrices.

Best,

Ric