When we multiply a matrix by a scalar (i.e., a single number) we simply multiply all the matrix's terms by that scalar. We can also multiply a matrix by another matrix, but this process is more complicated. …

Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication.

So you're not just blindly doing some-- matrix-matrix products can be pretty tedious, but now you know what they're for. They're actually for the composition of two transformations where each of A and B …

The dot product of those column vectors, each of the corresponding column vectors, with your matrix X. So these are both completely valid interpretations, and hopefully this video at least gives you a …

You take this x and you multiply it by this matrix, you're going to get its projection onto the L, onto the line. If you take this vector, let's say a, and you multiply it times this matrix right there, you're going to …

Learn about the conditions for matrix multiplication to be defined, and about the dimensions of the product of two matrices.

Matrix multiplication is intimately connected to linear transformations. In fact, matrix multiplication can be thought of as a way of representing and performing linear transformations.

If you view them each as vectors, and you have some familiarity with the dot product, we're essentially going to take the dot product of that and that. And if you have no idea what that is, I'm about to show …

The identity matrix plays a similar role in operations with matrices as the number 1 plays in operations with real numbers. Let's take a look.

Learn about the dot product and how it measures the relative direction of two vectors.