Conjugate transpose: Difference between revisions

Revision as of 11:27, 26 March 2024

Revision as of 07:44, 9 May 2024

Line 68:

<math>

e^{i\theta} = \begin{pmatrix} \cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta \end{pmatrix} = \cos \theta \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} + \sin \theta \begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}.

</math>

Line 77:

<math>

1 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \quad i = \begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}.

</math>

A general complex number <math>z=x+iy</math> is then represented as

<math>

z = \begin{pmatrix} x & -y \\ -y & x \end{pmatrix}.

</math>

The complex conjugate operation, where i→−i, is seen to be just the matrix transpose.