Purpose of Inverse...


I was wondering what is the purpose of calculating the inverse of a matrix. I know the mathematics behind it and how it’s done, etc. But, in newbie terms, what is the purpose of actually using it?



It allows you to get back from post-matrix-multiplication vectors/co-ordinates to the original input vector/co-ordinates. In other words, it allows you to do the inverse of the transformation represented in the original matrix.

This only works for invertable matrices of course.



Say you have a matrix A. Since you can multiply A times things, you want to also be able to divide things by A. So for another matrix B, B/A is defined as B*(1/A), and 1/A is defined to be the matrix so that A*(1/A) == 1 (actually not one, but the identity matrix). I.E. 1/A is the inverse of A.

Unfortunately not all matrices have this property, so you can’t do all the fancy arithmetic with matrices that you can with numbers.