Did you know SD-WANs can improve network connectivity? Check out this webinar to learn how an SD-WAN simplified, one-click tool can help you migrate and manage data in the cloud.

Become a Premium Member and unlock a new, free course in leading technologies each month.

Solved

Posted on 2009-04-07

W is a subspace in R^n. T is a linear operator on R^n defined by T(v)= w-z, where v= w+z, w in W, and z in W-perp. (v, w, z are vectors)

Prove T is an orthogonal operator.

Prove T is an orthogonal operator.

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

- Help others & share knowledge
- Earn cash & points
- Learn & ask questions

1 Comment

So let T(u)=w-z, and T(v)=w'-z'

Then

<T(u), T(v)>

= <w-z, w'-z'>

= <w,w'> - <w,z'> - <z,w'> + <z,z'>

= <w,w'> + <w,z'> + <z,w'> + <z,z'> (because <z,w'>=<w,z'>=0)

= <w+z, w'+z'>

= <u, v>

Q.E.D.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Course of the Month7 days, 6 hours left to enroll

Earn Certification

Lean Six Sigma Yellow Belt

$99.00$89.10

Join the community of 500,000 technology professionals and ask your questions.