Multiply matrices by scalars to produce new matrices, for example, when all of the payoffs in a game are doubled.
We know what you're thinking. What the heck is a scalar? Scalar is a fancy-panties way of saying number. By number we mean any of these things:
You can multiply any of these babies through a matrix with ease. Take this matrix:
Her name is S. We need to find 3S. Here's how that looks:
3S is really just 3 multiplied through the matrix:
Moving on, there are more complicated examples of scalar multiplication. For example, we already know our matrix, S. This one is K:
How do we find this?
2K + S
Basically, we just plug the matrices in for their variables and go:
We multiply the 2 through the K matrix first:
Then we're ready to just add the two matrices. We remember how to do that, of course; we just add the entries in each location:
As long as your matrices are the same size for addition and subtraction purposes, it's all good.