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Give a good explanation of determinants?

  1. Feb 25, 2009 #1
    I don't think this goes under H/W questions, as it's not a specific question needing solving, or a proof, etc.
    Getting back to the point, anyone know any good websites or sources that give a good explanation of determinants? I mean what they do, why they do it, not just how to do it. I googled and got pretty boring stuff that tended to be either simply how to do them or just...well... lacking excitment.
  2. jcsd
  3. Feb 25, 2009 #2
    Re: Determinants

    Try to understand the formal properties (multilinearity) in terms of the interpretation as the volume of the parallelogram/parallelepiped (see the http://en.wikipedia.org/wiki/Determinant" [Broken]).
    Determinants may not be the most exciting thing you will ever learn, but absolutely essential in almost all fields of math and applications of math.
    Last edited by a moderator: May 4, 2017
  4. Feb 25, 2009 #3
    Re: Determinants

    If you want to know why the determinant does what it does, pick up 'Analysis on Manifolds' by Munkres.
  5. Feb 26, 2009 #4
    Re: Determinants

    Cheers guys
    I know what you mean by not the most exciting thing! Blimey, but I kind of get what you mean by important. I came across determinants reading about vectors.
    Thanks again.
  6. Feb 26, 2009 #5

    Ben Niehoff

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    Gold Member

    Re: Determinants

    The determinant of an NxN matrix is equal to the oriented volume of the N-parallelepiped defined by the N column vectors (or alternatively, the N row vectors) of that matrix.

    So for example, if you have a parallelogram defined by two vectors in the plane, (1,2) and (-1,3), then the area of this parallelogram is given by

    [tex]A = \left| \begin{array}{rr}1 & -1 \\ 2 & 3 \end{array} \right| = (1)(3) - (-1)(2) = 5[/tex]

    which you can check geometrically, if you like.
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