Matrices are a special type of vector in R. So there's, they're not a spe, a different, a separate class of objects. But they're basically vectors that have a sp, an attribute called the di, called the dimension. And so the dimension attribute is an integer vector of length two. Where the first number is the number of rows the matrix, and the second number is the number of columns. And so, if I can create a matrix empty matrix with the matrix function, and I can explicitly say how many rows and how many columns there are. This is not the only way to create a matrix, but it's one way. And so when I auto print the matrix by typing the, the object m and hitting Enter, you'll see that it'll show me that, first of all the matrix is full, is initialized with NA values. There's no values in here. And you can see that there's two rows and three columns and they're labeled by the numbers in the brackets. If I call the dim function on m, it'll give me the dimension attribute, which in this case it says there are two rows and three columns, because the first rows are number rows and the second number, sorry excuse me. The first number is the number of rows and the second number is the number of columns. If I call the attributes function on m, you'll see it returns a list where the first element is the dim element and it has the vector 2,3. So these are all aspects of a matrix which is a vector that has a dimension attribute to it. Matrices are constructed column wise. So you can think of the matrix taking a vector and all the numbers are inserted into the matrix by, by column. So the first column gets filled and then when you hit the number of maximum number of rows, then the second column gets filled and the third column et cetera. So if I create a matrix by taking the sequence 1 to 6 and then I say, I specifies that it has two rows and three columns. Well, how does this matrix get constructed? So the way, it gets constructed column wise. So the first thing it happens is it takes 1, 2, and now there's only two rows, so it can only go to 2. And then that makes the first column. The second column is made up of 3, 4. And then the third column is made up of 5 and 6. You can also create a matrix by creating the dimension attribute on a vector. So, for example, I can take, I can create a vector that's a sequence 1 to 10. And then add the dimension attribute to it. So here, I'm using the dim function, but I'm assigning a value to the dim attribute of m. So here I'm assigning the vector 2,5. So what I'm saying is, I want to take this vector and transform it into a matrix that is two rows and five columns. And so now after I've done that, I've got a matrix m, which has two rows and five columns and it's filled in the matrix column wise. Another way to create a matrix, and this is a common way, is by binding columns or binding rows. And so you, this is column, column binding and row binding can be achieved by the fu, the functions c-bind and r-bind. So for example, suppose I have the two objects x, which is sequenced from 1 to 3 and y, which is a sequence from 10 to 12. If I cbind those two objects, then I'll get a, I'll get a matrix where the first column is 1 to 3, and the second column is 10 to 12. So this is kind of what you might expect would happen. If I rbind those two objects, then the first row will be 1 to 3, and the second row will be 10 through 12. So cbind-ing and rbind--ing is another way to create a matrix.
