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Questions about matrices and vectors:Why does the dot product of

  1. Oct 15, 2008 #1
    Questions about matrices and vectors:


    Why does the dot product of a and b equal |a||b|cos(angle between a and b)

    are the vectors of a matrix the columns or the rows, or can it be either?

    I know a 0 determinant of a matrix means the vectors lie on top of eachother, and the absolute value of a determinant is the area of the shape formed by a,b, and a+b, but what is the geometrical meaning of a negative versus a positive determinant?

    Seing as the dot product of vectors has a geometrical interperetation, im wondering what is the geometrical interperetation of matrix multiplication.
     
  2. jcsd
  3. Oct 16, 2008 #2

    JasonRox

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    Re: matrices

    Try looking at cases where the determinant is positive and those negative. After about 3 examples, you might get an idea.

    Or look at the equation |a||b|cos(angle ab), when is it negative? It is negative when cos is negative, and when is that?
     
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