June 9, 2013
Ok so we’ve cover matrix transpose and multiplication, we’re now going to get into determinants. I’ll spread this into multiple posts as we’ll be eventually dealing with recursive functions. Determinants are a crucial glue in matrix math which allow you to find the inverse, which is akin to the reciprocal.
With the a 2 x 2 matrix, the determinant is single function – once we deal 3 x 3 and greater sized matrices we essentially recursively break them down to 2 x 2 and pass the base function. For a 2 x 2 matrix:
All we need to do is multiply the first element of the first row by the last element of the last row (A*D), and first element of the last row by the last element of the first row (C * B). Then take these away from each other (AD) – (CD) to give us our determinant:
(1*1) = 1
(4*2) = 8
(1-8) = -7
We’ll dig into 3 x 3 matrices next and then onto recursive methods…