How Can You Represent Determinants Using Permutations?

[jtceleron]

it seems to have many different ways to express a determinant, when we are using indices to write vectors and tensors, e.g. in General Relativity. is there any summary about how to express a determinant, for example, in Levi-Civita Tensor and so on?

 

[chiro]

Hey jtceleron.

You can indeed represent a determinant in terms of permutations.

http://en.wikipedia.org/wiki/Determinant#Levi-Civita_symbol

If you want a bit more of a discourse on determinants, one book I have read in the past has a chapter dedicated to determinants and its this book:

https://www.amazon.com/dp/940072635X/?tag=pfamazon01-20

This books looks at the construction and properties of general determinant functions.