Understanding Odd and Even Permutations in Linear Algebra - Quick Help

[elle]

Linear Algebra help -urgent!

Hi,
I'm doing a bit of self learning on Linear Algebra but I'm kinda confused with the information given on odd and even permutations?

How do you determine whether a permutation is odd or even?

For example, the book has given some examples such as:

(1 2 3 4) is odd, (1 3)(2 4) is even?

Can someone help please? Thank you!

 

[radou]

Try to count the 'steps' you need to do a permutation and see if the number is odd or even.

 

[buzzmath]

A permutation is even if it's the product of an even number of 2-cycles. That's why (1 3)(2 4) is even. A permutation is odd if it isn't even. (1 2 3 4 ) written as two cycles would be (1 4)(1 3)(1 2) which is odd.

 

[elle]

Thanks guys! I get it now