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Math Help - how to determine sigma and sgn(sigma) for matrices

  1. #1
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    how to determine sigma and sgn(sigma) for matrices

    As the topic says, I don't know how to determine sgn(\sigma) or  \sigma for any n x m matrix

    I know this section falls under determinants but I am kind of having a hard time finding online resources for this section
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  2. #2
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    I thought I new matrices pretty well, but you will have to tell me what " \sigma" represents. At a guess, I might take it to mean the permutations used in defining the determinant of a matrix:

    The determinant of an n by n matrix can be defined as \sum (-1)^{sgn(\sigma)}a_{1, \sigma(1)}a_{2,\sigma(2)}\cdot\cdot\cdot a_{n, \sigma(n)}.
    Where \sigma is a permutation of {1, 2, 3, ..., n}, [tex]sgn(\sigma)[/itex] is 1 if  sigma is an even permutation, -1 if it is an odd permutation, and the sum is take over all such permutations.

    But that doesn't make sense, nor does your "I know this section falls under determinants", because an "n by m matrix" only has a determinant if m= n.
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  3. #3
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    sorry my question was asked rather incorrectly

    in one of the examples i took down in class our proffessor asked us to determine the [tex]sgn(\sigma)[\MATH]

    where eg \sigma =

    [1 2 3
    3 2 1]

    a 2x3 matrix

    i dont know how to solve this or what significance this has with matrices

    im sorry if my english isn't good
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