Results 1 to 4 of 4

Math Help - Inner product inequality sort of?

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    195

    Inner product inequality sort of?



    Okay. The left side is clearly <a,b>. The right side is...um?

    Let j = (1,2,...,n) and k = (1,1/2,...,1/n), then <sqrt(j),a><sqrt(k),b>.

    I guess? I don't have any idea what to do with this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Since the indices are the same the scalar j can cancel out as every term of the first sum will have (1/j) and every term of the second will have a j. It is simply the Cauchy-Schwarz inequality now.

    Cauchy?Schwarz inequality - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by Jameson View Post
    Since the indices are the same the scalar j can cancel out as every term of the first sum will have (1/j) and every term of the second will have a j. It is simply the Cauchy-Schwarz inequality now.

    Cauchy?Schwarz inequality - Wikipedia, the free encyclopedia
    I'm not sure that this holds. Notice the difference between:

    \sum_{j=1}^n j(a_j) \sum_{j=1}^n {b_j \over j}

    and

    \sum_{j=1}^n j(a_j){b_j \over j}<br />
    Last edited by davismj; November 5th 2009 at 08:59 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Yes, of course. Got too excited to post a cool link. Won't work.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. product inequality question
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 7th 2011, 08:06 PM
  2. infinite product (sort of)
    Posted in the Math Challenge Problems Forum
    Replies: 5
    Last Post: March 16th 2011, 09:17 AM
  3. An inequality with a product of two sums
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 25th 2011, 03:42 PM
  4. What sort of DE is this?
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: November 1st 2010, 02:24 AM
  5. Question about inner product space inequality
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 24th 2009, 07:37 PM

Search Tags


/mathhelpforum @mathhelpforum