how to determine sigma and sgn(sigma) for matrices

**Lutz** · May 16th 2010, 05:56 AM

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

**HallsofIvy** · May 16th 2010, 06:07 AM

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.

**Lutz** · May 16th 2010, 11:12 AM

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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