Can you show me please trace|a><b|=<b|a>

[tchem]

Can you show me please trace|a><b|=<b|a> . Thank you?

 

[tchem]

Projector

How can we show that the eigenvalues of a projector are 1 or 0? Thank you

 

[tchem]

Unitary

How can we show that the eigenvalues of a unitary operator are complex numbers of unit norm. Thank you

 

[christianjb]

You should really show an attempt at the question, but:

Tr[ |a><b| ] = sum <ci|a><b|ci>=sum<b|ci><ci|a>=<b|a>

 

[tchem]

Anti-Hermition

A is anti-hermition;
please show that <b|A|b> is a pure imaginary number for any |b> in the state space

 

[tchem]

Trace

How can we show;
trace A= sum<ei|A|ei>=sum<fi|A|>fi

 

[berkeman]

tchem, as christianjb points out, you MUST show your own work so far, in order for us to be of help with your homework and coursework. We do not do your work for you here on the PF. Please post your work and thoughts so far for each of the multiple questions you are asking.

 

[tchem]

actually, I solved the questions of unitary and anti-hermition, but I cannot prove that the eigenvalues of projector can be 0 or 1 . I get the point and guess it from the exact definition of projection operator however I cannot get it into writing mathematically

 

[George Jones]

actually, I solved the questions of unitary and anti-hermition, but I cannot prove that the eigenvalues of projector can be 0 or 1 . I get the point and guess it from the exact definition of projection operator however I cannot get it into writing mathematically

What is the exact definition of a projection operator?