Matrix Vector multiplication.

We've learned about matrix addition, matrix subtraction, matrix multiplication.

learned matrix multiplication, why that happens.

That's how mm, matrix multiplication works.

Matrix multiplication is really useful since you can pack a lot of computation into just one matrix multiplication operation.

Does the order of the matrix multiplication matter?

It turns out that matrix multiplication is associative.

So that's it for the properties of matrix multiplication.

In this video we talk about matrix, matrix multiplication or how to multiply two matrices together.

Finally let me show you one more neat trick you can do with matrix matrix multiplication.

It's important when we're doing matrix multiplication, to confirm that it matters what direction you do the multiplication in.

Then in the second segment, I'll review some matrix algebra, because I'm assuming not everybody is familiar with matrix algebra particularly, matrix multiplication.

And keep in mind, these are human created definitions for matrix multiplication.

And so we say that matrix multiplication does enjoy the associative property.

We'll start with a special case of that, of matrix vector multiplication multiplying a matrix together with a vector.

Just as a quick aside, if you're familiar with matrix multiplication, there is a very nice connection between this little algorithm that we're just working on and matrix multiplication.

And it's important to realize when we're doing matrix multiplication, that direction matters.

It's going to add all those up. That's exactly what matrix multiplication does.

But, in the next video we're going to take this and generalize this to the case of matrix matrix multiplication.

Where data matrix is this thing here, and parameters is this thing here, and this times is a matrix vector multiplication.

line of code assuming you have an appropriate library to do matrix vector multiplication.

So the way that we've defined matrix multiplication, you cannot multiply these two matrices.

And then, remember that to do matrix multiplication, the two matrices have to be conformable.

In this video I want to tell you about a few properties of matrix multiplication.

So, this is the same matrix vector multiplication as you saw in the last videos.

When we talk about that algorithm, it turns out that matrix, matrix multiplication is one of the key steps that you need to know.

So, we say that matrix multiplication is not commutative, it's a fancy way of saying it.

In this video we'll talk about matrix addition and subtraction, as well as how to multiply a matrix by a number, also called Scalar Multiplication.

In this case they clearly do not equal each other, so matrix multiplication is not defined here.

Multiplication

Multiplication

Multiplication

Multiplication

In matrix multiplication, the way we fill in the I J entry of the product, we take the I row of the first matrix and J column of the second matrix and I always need two hands whenever I think about matrix multiplication and you across this one and down this one at the same time.

So one matrix multiplications that you manage to make 12 predictions and, even better, it turns out that in order to do that matrix multiplication and there are

The only way that we know to define matrix multiplication is if these middle two numbers are the same.

Often domain specific languages allow you to express things like matrix transposition or multiplication at a very high level.

Multiplication Puzzle

Enable Multiplication

This multiplication.

Karatsuba multiplication.

So where do we see multiplication we have a multiplication, a division, a multiplication again.

Let's do some more matrix multiplication examples, because I think it is all about seeing as many examples as possible.

It overloads operators like addition, subtraction, multiplication, and even computes the transpose of a matrix, and in some more extended code, it can actually invert a matrix using Cholesky factorization.

Matrix A. Here's my Matrix