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What is the square of a column vector?

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Hi,

    Is there a matrix property that can be applied to take the square of a column vector?

    Something like:

    [itex]{\bf x}=\left[x_1,x_2,x_3\right]^T[/itex]
    [itex]\left[{\bf x}\right]^2[/itex]
    [itex]={\bf x}{\bf x}^T[/itex]
    or
    [itex]={\bf x}^T{\bf x}[/itex]?

    Thank you.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 20, 2011 #2

    SammyS

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    What is the size of the matrix: [itex]={\bf x}{\bf x}^T\,?[/itex]

    What is the size of the matrix: [itex]={\bf x}^T{\bf x}\,?[/itex]
     
  4. Nov 20, 2011 #3
    Hi SammyS,

    [itex]{\bf x}{\bf x}^T[/itex] is 3x3
    while
    [itex]{\bf x}^T{\bf x}[/itex] is 1x1
     
  5. Nov 20, 2011 #4
    I'm not sure what you mean by the square of a column vector...
     
  6. Nov 21, 2011 #5

    SammyS

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    Generally the square of a vector refers to the scalar product, which you can crudely think of as a 1 by 1 matrix. Therefore, the answer is (xT)x .
     
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