# Dirac notation

## Homework Statement

Hi

Please take a look at the following equality found in my book:

$$\left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v} \mathrel{\left | {\vphantom {v \mu }} \right. \kern-\nulldelimiterspace} {\mu } \right\rangle } = \sum\limits_v {\left\langle {\mu } \mathrel{\left | {\vphantom {\mu v}} \right. \kern-\nulldelimiterspace} {v} \right\rangle ^* \left| v \right\rangle }$$

The asterix denotes complex conjugation. I cannot see why the second equality holds, since

$$\sum\limits_v {\left\langle {\mu } \mathrel{\left | {\vphantom {\mu v}} \right. \kern-\nulldelimiterspace} {v} \right\rangle ^* \left| v \right\rangle } = \sum\limits_v {\left\langle {v} \mathrel{\left | {\vphantom {v \mu }} \right. \kern-\nulldelimiterspace} {\mu } \right\rangle \left| v \right\rangle } \ne \sum\limits_v {\left| v \right\rangle \left\langle {v} \mathrel{\left | {\vphantom {v \mu }} \right. \kern-\nulldelimiterspace} {\mu } \right\rangle }$$

What am I missing here?

Best,
Niles.

vela
Staff Emeritus