Help me understand a pair of sequences

[honhungoc]

Pls help

I hv a query, pls expain it for me

We hv two sequence A and B

A=[x1, -x2*]
B=[x2, x1*]

Could you please tell me why the inner product of 2 sequences A and B is zero?

A.B= x1x2* - x2*x1 = 0?

Thank u

 

[Jyotshna Mamillapalli]

Re: Pls help

what does * indicate?

 

[hamidrezakarami]

Re: Pls help

when We have two sequence A and B

A=[x1, -x2*]
B=[x2, x1*]

A.B /= x1x2* - x2*x1 = 0? !!!!!!!!!!!!!
A.B = x1.x2 - x2*x1*

so, if x1 and x2 are real then A.B = 0

 

[alisha]

Re: Pls help

A and B contain elements which r complex conjgates of one another when dier scaler product is taken da result is zeron dats da condition for orthogonality of 2 complex thingie whether dey r vectors, signals or smthign else!!

 

[LouisSheffield]

Pls help

hinhungoc

I don't think your equation A.B= x1x2* - x2*x1 reflects your problem:
A=[x1, -x2*]
B=[x2, x1*]

Wouldn't it be A.B= x1x2 - x2*x1*??

If not, do you have a mistake with your vectors A or B?

Added after 7 minutes:

honhungoc (sorry about the misspelling)

If your vectors are (rather):
A=[x1,-x2*] and
B=[x2*,x1], then the dot becomes x1x2* - x2*x1 as you indicated in your post.

If so, this does have to be zero, because multiplication of complex numbers is commutative.
(i.e. x1x2* = x2*x1, so x1x2* - x2*x1 = x1x2* - x1x2* = 0)