Results 1 to 2 of 2

Math Help - Hilbert Spaces: Prove Vo is a subspace

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    10

    Red face Hilbert Spaces: Prove Vo is a subspace

    Let V be a vector space over C with a pre-inner product <v,w>
    Let ||v|| be the semi-norm ||v|| = <v, v>.
    (i) Show that Vo = {v element of V : ||v|| = 0} is a subspace of V .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by dazed View Post
    Let V be a vector space over C with a pre-inner product <v,w>
    Let ||v|| be the semi-norm ||v|| = <v, v>.
    (i) Show that Vo = {v element of V : ||v|| = 0} is a subspace of V .
    Hint: The Cauchy–Schwarz inequality |\langle v,w\rangle|\leqslant\|v\|\|w\| holds in a pre-inner-product space.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Hilbert spaces
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 16th 2011, 12:53 AM
  2. Hilbert Spaces Proof
    Posted in the Differential Geometry Forum
    Replies: 10
    Last Post: May 11th 2010, 01:04 AM
  3. Hilbert spaces
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 25th 2009, 09:31 AM
  4. Hilbert spaces -urgent
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 15th 2009, 10:28 AM
  5. Hilbert Spaces
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 13th 2009, 10:27 AM

Search Tags


/mathhelpforum @mathhelpforum