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Function notation question

  1. Jun 19, 2011 #1
    1. The problem statement, all variables and given/known data
    I have this problem, but I'm not familiar with the function notation that the professor is using. Can anyone tell me what is actually being asked? I understand everything up to the part that is in bold, but after that, I am lost.

    Some of the formating was lost so Rn is shown as R^n and xT is x transpose.
     
  2. jcsd
  3. Jun 19, 2011 #2

    LCKurtz

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    x and y are in Rn, so they are n by 1 matrices so xTAy is (1 by n)(n by n)(n by 1) = 1 by 1 or scalar. If you put in A = BTB I think you will see that it is a dot product of two vectors if you look at it right.
     
  4. Jun 19, 2011 #3

    Fredrik

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    I would interpret the problem as "Show that d satisfies the definition of an inner product". This is really easy if you know the definition and you're comfortable with matrix algebra (stuff like [itex](XY)^T=Y^T X^T[/itex]).

    If you're only supposed to show that [itex]x^TAy[/itex] is a dot product of two vectors, the complete solution would be [itex]x^TAy=x^T(Ay)[/itex], because Ay is a column vector. (You know that the definition of matrix multiplication implies that [itex]u^Tv=u_1v_1+\dots+u_nv_n[/itex] when u and v are column matrices, right?)
     
    Last edited: Jun 19, 2011
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