I"ve been given a vector room of linear polynomials in x, $p(x)=ax+b,;;$ $q(x)=cx+d$, and the inner product is characterized to it is in $langle p,q angle=ac+bd$. I"ve been able to verify all the axioms for the inner product other than for the complicated conjugate one, $langle p,q angle^*=langle q,p angle$, where $p$ and $q$ room vectors.

The issue I"m having is that ns don"t understand how the complicated conjugate can apply if there isn"t an $i$ in the equation. All I understand is that the facility conjugate take away the type $(ax+iy)^*=ax-iy$, however I"m really confused regarding what this way without $i$.

What is the complicated conjugate the a vector that doesn"t have actually an imagine component?


If your base field is $ptcouncil.netbbR$, so that $a$, $b$, $c$, $d$ are real, the facility conjugate that a genuine number is the number itself: $a^*=a$, and also the relation is clear satisfied.

You are watching: What is the complex conjugate of vector a

If you take it $ptcouncil.netbbC$ as the base field, friend must consider the coefficients as complex numbers: if $a=x+yi$ with $x,,yinptcouncil.netbbR$, then $a^*=x-yi$. In the case, friend should specify your within product together $langle p,q angle = ac^* + bd^*$.


Thanks because that contributing an answer to ptcouncil.netematics Stack Exchange!

Please be certain to answer the question. Administer details and also share your research!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; earlier them increase with references or an individual experience.

Use ptcouncil.netJax to layout equations. ptcouncil.netJax reference.

See more: How To Get Rid Of Fetish : Nostupidquestions, Dear Ibby, Can You Get Rid Of A Fetish

To discover more, view our advice on writing great answers.

short article Your prize Discard

By clicking “Post her Answer”, girlfriend agree come our terms of service, privacy policy and also cookie policy

Not the answer you're looking for? Browse other questions tagged linear-algebra inner-products or questioning your own question.


site architecture / logo © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.2.40634

ptcouncil.netematics ridge Exchange works best with JavaScript enabled

your privacy

By click “Accept all cookies”, girlfriend agree ridge Exchange deserve to store cookies on your an equipment and disclose info in accordance v our Cookie Policy.