CHAPTER 01.08: INTRODUCTION: What is an identity matrix?
So letís see what an identity matrix is. An identity matrix is a square matrix. An n by n matrix A is called an identity matrix if AIJ is equal to 0 for I not equal to J for all I, J. And AII is equal to 1. I is equal to 1 up to N. So what we are saying here is that an identity matrix is where your non diagonal element, they are all 0 just like in a diagonal matrix but you also need to have-only †one is on the diagonal- so all the diagonal elements are to be 1. And thatís what we need in an identity matrix.
†So letís take an example here. So letís suppose I have a matrix which looks like this. †1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1. So that is an identity matrix because what you are †finding out here is that any of the elements, which are not on the diagonal they are zero-thatís what †we mean by I not equal to J. If you look at the element numbers of these elements, you will find the row numbers are not the same as the column number. But when the row number is the same as the column number, which are also the diagonal elements, here you will find out you only have 1 there. So that is what we mean by identity matrix. And that is the end of this segment.