CHAPTER 01.08: INTRODUCTION: What is an identity matrix? So let’s 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 that’s what we need in an identity matrix. So let’s
take an example here. So let’s 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-that’s 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. |