Let V be a real or complex vector space (possibly infinite-dimensional), and let 3 be a

Chapter 6, Problem 22

(choose chapter or problem)

Let V be a real or complex vector space (possibly infinite-dimensional), and let 3 be a basis for V. For x.y E V there exist v\,v2.... ,v E ft such that Define x = 2_]a i v i an( i y = /^hVjI I i=\ fay) = ])2"i.bi. (a) Prove that ( ) is an inner product, on V and that 0 is ail orthonormal basis for V. Thus every real or complex vector space; may be regarded as an inner product space. (b) Prove that if V R" or V = C" and ft is the standard ordered basis, then the inner product, defined above is the standard inner product.

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back