Results 1 to 5 of 5

Math Help - Matrix (vector) multiplication

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    3

    Matrix (vector) multiplication

    Hi MHF,

    Consider 2 vectors x and m with the same dimension. Is the following condition true?
    (x - m)(x - m)^T == xx^T - mm^T

    It has been a while since I did linear algebra so some help is much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    It is true. As x and m have the same dimension say pxq, simply multiply out each side of your equation, you should get pxp in both cases.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by ikkuh View Post
    Consider 2 vectors x and m with the same dimension. Is the following condition true?
    (x - m)(x - m)^T == xx^T - mm^T
    It is quite possible that I have misread your post.
    But I do not agree that it is true.
    Consider: M=<-2,4>~\&~X=<3,-6>.
    Is that a counter-example?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    The dimensions of the solutions may be the same, maybe not the solution itself.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2011
    Posts
    3
    Quote Originally Posted by pickslides View Post
    The dimensions of the solutions may be the same, maybe not the solution itself.
    That is exactly what I was thinking. Unfortunately problem I need to solve is this:
    S = \frac{1}{n-1}\sum\limits_{i=1}^n ({\bf x}_i - {\bf m})({\bf x}_i - {\bf m})^T where
    {\bf m} = \frac{1}{n}\sum\limits_{i=1}^n x_i
    Prove that the expression for the covariance matrix (above) can be rewritten as:
    S = \frac{(\sum\limits_{i=1}^n {\bf x}_i {\bf x}_i^T) - n {\bf m}{\bf m}^t }{n-1}

    I might have split the question wrong before. Anyone who sees now how you can rewrite the expression?
    Last edited by ikkuh; May 22nd 2011 at 05:46 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Matrix Notation and Matrix Multiplication
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: February 11th 2011, 04:57 AM
  2. [SOLVED] Vector and matrix multiplication
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 6th 2010, 10:24 AM
  3. Matrix and vector multiplication
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 7th 2010, 07:02 AM
  4. multiplication of two matrix
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 19th 2010, 02:53 PM
  5. vector multiplication
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: September 9th 2008, 09:32 PM

Search Tags


/mathhelpforum @mathhelpforum