Determinants: The analytics
In this video I define the general determinant on R^(n by n) as a multilinear and alternating function. From these simple properties, I derive most of the commonly used properties of the determinant in a straightforward fashion without having to bother with an explicit formula. Finally, I derive the 3-by-3 case, and from this generalize to the formulae for column and row expansions. An example illustrates how polynomials can be understood as determinants of a specific n-by-n matrix.