Hermitian and unitary show all its eigen values are ±1

[debjit625]

Homework Statement

If a matrix is both Hermitian and unitary show all its eigen values are ±1

Have no idea how to solve ,Have an idea what's hermitian and unitary matrix
I know eigen values of hermitian matrix are real and for a unitary matrix it on a unit circle .

Thanks

 

[BvU]

Good. Now write out in expressions (formulas) what this means for the wave function. And don't erase the template.

 

[PeroK]

Homework Statement

If a matrix is both Hermitian and unitary show all its eigen values are ±1

Have no idea how to solve ,Have an idea what's hermitian and unitary matrix
I know eigen values of hermitian matrix are real and for a unitary matrix it on a unit circle .

Thanks

How many real points are there on the unit circle?

 

[BvU]

 

[debjit625]

Well I am sorry I erase the template,will not happen again.
But now the main thing

Have no idea how to solve

so that means I have no idea ,now that states my problem very well.

what this means for the wave function

what you are taking about I have no idea I am in first year and we just started learning these..

How many real points are there on the unit circle?

I guess infinite but what I meant was that they are all at a distance 1 unit from the center.

I would appreciate a proper help/hint from you guys ,these are not helping me at all

 

[BvU]

We do what we can but apparently have no good idea about your situation. You ask something that looks pretty advanced but can't tell how many points on the unit circle in the complex plane are real. So tell us a little more -- what course is this ? Math, quantum mechanics, ?

Your

I know eigen values of hermitian matrix are real and for a unitary matrix it on a unit circle .

perhaps gave us the wrong impression. Do you know what unit circle ?

 

[debjit625]

If anybody wants to know the answer
http://math.stackexchange.com/questions/1883453/if-a-matrix-is-both-hermitian-and-unitary-show-all-its-eigen-values-are-±1