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Positive definitive matrix in wikipedia

  1. May 11, 2012 #1
    Hi all. I have a quick question

    In this wikilink en.wikipedia.org/wiki/Positive-definite_matrix in the first example

    I don't get how they get 2x1^2 -2x1x2+2x2^2-2x2x3+2x3^2 in the third line.

    Can anyone bother to explain?

    Thanks a lot
  2. jcsd
  3. May 11, 2012 #2


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    Science Advisor

    Hey de_student and welcome to the forums.

    For that line they are multiplying a row vector by a column vector which translates to an inner product. So if the row vector is [a, b, c] and the column vector is [x, y, z]^T then the result will be ax + by + cz using the standard definition of matrix multiplication.
  4. May 11, 2012 #3
    Hi. Thanks for prompt answer. But my question is in the example there is not always [c]-member from row vector. like there is no x3 in the member (2x1-x2). How can I deal with that?
  5. May 11, 2012 #4


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    I'm not sure what you mean, but the expression has been expanded out in the right manner. The reason there is no x3 for this term is because the M matrix has a 0 element at row 3, column 1. This is why there is no x3 element for this particular case in that particular cell.
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