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What is the essence of determinant?

  1. Aug 29, 2011 #1
    the definition of a determinant is not simple at the first sight

    however we still have extremely simple relation det(AB)=det(A)det(B)

    it seems that the grassmann algebra is the essence behind determinant, isn't it?
  2. jcsd
  3. Aug 29, 2011 #2
    Part of the problem is that a matrix can represent many different (and intrinsically different) things: a system of linear equations; a linear transformatio; the adjacency
    relation in a graph, etc. , so I don't think a single interpretation for det is reasonable.

    Do you have a particular use/context for a matrix in mind?
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