Results 1 to 2 of 2

Math Help - Using CS inequality

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    4

    Using CS inequality

    I need to show that if \bf{M} is an m \times n matrix, then ||\bf{M}(\bf{h})||\leq \alpha ||\bf{h}|| for some \alpha by estimating the entries of \bf{M}. The hint I am given is that \bf{M}(\bf{h}) = \bf{y} = (y_1, \ldots, y_m) where y_i=\bf{m}_i \cdot \bf{h} for some \bf{m}_i \in R^n and apply the CS inequality.

    I have not done multivariable calc in a VERY long time, and I just can't seem to jumpstart my brain to attack this problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    675
    Thanks
    32
    If we denote by (a_{k,j})_{1\leq k\leq m,1\leq j\leq n} the coefficients of the matrix M, we have to notice that y_i =\sum_{j=1}^na_{ij}h_j. Now, the question is: what is the vector m_i and what does the Cauchy-Schwarz inequality give?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2011, 08:20 PM
  2. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  3. inequality
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 26th 2010, 04:34 AM
  4. inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 24th 2010, 12:08 PM
  5. Inequality
    Posted in the Algebra Forum
    Replies: 0
    Last Post: October 8th 2009, 03:06 AM

Search Tags


/mathhelpforum @mathhelpforum