We’ve already introduced some of the topics of Group Theory. In this entry we’ll talk about Lagrange’s Theorem, various morphisms, and try to tie it back to our ongoing discussion of permutations. We’ll also give some examples of groups…
Here we prove that permutations can be divided into even permutations and odd permutations. We’ll also go over what happens when you compose two permutations. Surprisingly, it behaves like adding numbers. E.g. composing an even permutation with an odd permutation results in an odd permutation. Two odd permutations result in an even permutation, etc…
The dot product is so fundamental to linear algebra that it’s easy to take for granted that it works. Here we take a quick look at some of it’s potential by showing how it can be used to calculate the angle between two vectors.
A permutation is a function from a set into itself that is both 1 - 1 and onto. You probably know what those terms mean already, but just to refresh, a function is said to be one to one (1-1) if f(x) = f(y) implies x = y.
