 In this final video for section 3.1 about matrix operations, I want to introduce one final operation for a matrix. Now this operation is only going to be defined for square matrices that is matrices of the form N by N. And this is called the trace of a matrix. We'll denote this TR of A. And the trace is simply going to be the sum of the diagonal entries of that matrix. So for example, let's take a two by two matrix and a four by four matrix. The trace of A would be the sum of the diagonal. So we look at the main diagonal two and four. We add those together and we get six. That gives us the trace. If we want to do the trace of B, we're going to add together the main diagonal, which are going to get four entries in this one since it's a four by four matrix. You're going to get nine plus nine plus six plus one, which adds up to B 25. And then that's the trace of the matrix. And that's all there is to it for traces here. We just add together the main diagonal entries. Now that seems so simple. It's like, wow, that was pretty simple. We have a whole video on that. That's amazing. But despite the simplicity of the trace function, it turns out the trace function is a very important function in linear algebra. And so despite its simplicity, it'll prove to be useful in the future. And that then brings us to the end of section 3.1.