Sparse matrix–vector multiplication

Okay kiddo, let's pretend you have a big list of numbers arranged in a square, like a huge table. But most of the numbers in the table are actually zero! This table is called a matrix, and when there are a lot of zeros, we call it a sparse matrix.

Now, let's pretend you have another list of numbers that is as long as one of the sides of the table. This list is called a vector.

If we wanted to multiply the matrix with this vector, we would have to do a lot of calculations because most of the numbers in the matrix are zeroes, and we don't need to do any calculations with zeroes.

So, what we do is ignore all of the zeroes in the matrix, and only multiply the non-zero numbers with the corresponding numbers from the vector. Then we add up the results of those multiplications. This is called a sparse matrix-vector multiplication.

It's like cleaning your room. You only need to pick up the toys that are on the floor, and you can leave the toys that are already in their toy box. In the same way, we only need to worry about the non-zero numbers in the matrix when we do this kind of multiplication.

And that's it! Sparse matrix-vector multiplication is a way to make calculations faster and easier when there are a lot of zeroes in the matrix.