# Thread: how to determine sigma and sgn(sigma) for matrices

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

As the topic says, I don't know how to determine $\displaystyle sgn(\sigma)$ or $\displaystyle \sigma$ 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

2. I thought I new matrices pretty well, but you will have to tell me what "$\displaystyle \sigma$" 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 $\displaystyle \sum (-1)^{sgn(\sigma)}a_{1, \sigma(1)}a_{2,\sigma(2)}\cdot\cdot\cdot a_{n, \sigma(n)}$.
Where $\displaystyle \sigma$ is a permutation of {1, 2, 3, ..., n}, [tex]sgn(\sigma)[/itex] is 1 if $\displaystyle sigma$ 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.

3. 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 $\displaystyle \sigma =$

[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