Hello, everyone. Welcome to our lecture, Using Python to Find the Transpose of a Matrix. In this video, I'm going to show you how to find the transpose of a square matrix, a non-square matrix, a column matrix, and a row matrix. In fact, we might also find the transpose of an identity matrix. You will soon realize that the transpose of identity matrix is equal to itself. Let me select this cell as a Markdown cell, then run it. Markdown cell here, or this I. We're going to find the transpose of identity matrix as well. We have this matrix here. Matrix M is a square matrix. If I want to look at it first, I can run it, is a square matrix, three by three matrix. To find the transpose of this matrix, you have two options. The first option is to say M.transpose, that's the word transpose, but it's a method, closing parenthesis at the end. It will change the line to rows and then rows to lines. You see the first line here, the first row, 3, 1, 2, become the column. The second row, 6, 4, 8, become the second column. Then the last row become the last column. You can also use capital T. Instead of writing the word transpose, you can just say that T. Both of them, you will get the same answer. This is for the square matrix M. Now, for the non-square matrix, this M thing is true. Our matrix L is non-square because it's a two by three. Let me see what L look like. Matrix L is two rows and three columns. We can still find the transpose of this matrix. I would type L.T, you see, it become three by two. So the number of rows is three, the number of column is two now. You can also do the same method that we used before. L.transpose, you will get the same answer. L.transpose, same result. Now, let's look at column matrix. In this thing, we have a column matrix here called N. N is a column matrix. Let's see what N looked like. N is a column matrix, three rows, one column. Now, if you want to find the transpose of this matrix, you can just type N.T. Now, row matrix, so let us transform one of these to a row matrix. Let me just copy this and then transform it to a row matrix. Here, I will say R equal this. Let me delete one of this equality. I'll just say R equal this. Let me just take this out and take this one out. Just one row, three columns. Let's see that. Now, you look at how R look like. R is right here, is a row matrix. Now, if you want to find the transpose of R, you can just type R.T, so it become a column matrix now. Now, identity matrix, we have a matrix, a three-by-three identity. If you take the transpose of this, you will still get the same thing. That's what the word identity stand for. It is identity for multiplications, and is also this one is equal to its transpose equal to itself. Same thing would be true if you say I.transpose, you will get the same thing back. In this lecture, we learn how to find the transpose of a square matrix, of a non-square matrix, of a column matrix, of a row matrix, and identity matrix. Thanks, everybody. I will see you in the next video.
