- #1

- 775

- 1

I am trying to prove that for any two vectors x,y in ##ℂ^{n}## the product ## \langle x,y \rangle = xAy^{*} ## is an inner product where ##A## is an ##n \times n## Hermitian matrix.

This is actually a generalized problem I created out of a simpler textbook problem so I am not even sure if this is true although I believe it is true.

I proved most of the axioms for an inner product space, except the axiom that ## \langle x,x \rangle > 0 ## if ## x ≠ 0 ##. This is giving me trouble, since I first had to prove that ##<x,x>## is real (which I have done) but am still having trouble to actually prove that it is positive.

Any tips? Thanks!

BiP

This is actually a generalized problem I created out of a simpler textbook problem so I am not even sure if this is true although I believe it is true.

I proved most of the axioms for an inner product space, except the axiom that ## \langle x,x \rangle > 0 ## if ## x ≠ 0 ##. This is giving me trouble, since I first had to prove that ##<x,x>## is real (which I have done) but am still having trouble to actually prove that it is positive.

Any tips? Thanks!

BiP

Last edited: