# Trace of an Outer Product

1. Jun 3, 2014

### kq6up

Is the trace of an outer product of a normalized state eq. (psi) equal to 1?

Thanks,
Chris Maness

2. Jun 3, 2014

### atyy

Last edited: Jun 3, 2014
3. Jun 3, 2014

### George Jones

Staff Emeritus
It would be good for you to calculate this.

Let $\left\{\left| \psi_i \right>\right\}$ be an orthonormal basis.

Steps:

1) express $\left| \psi \right>$ as an arbitrary linear combination of basis elements; 2) express the outer product in terms of this linear combination; 3) find the trace with respect to this basis.

You might need a few more hints.

4. Jun 3, 2014

### kq6up

I think I have it, but my LaTeX editor is giving me fits with this half bra-ket stuff. I will post it after I install MacTex on my new computer.

That will be a while 2.2Gb later.

Regards,
Chris Maness

5. Jun 3, 2014

### dextercioby

If you know the code, you can type LaTex here. We've got enabled through Mathjax.