Scalar Multiplication: One is the Loneliest Scalar?
We can 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-pants way of saying "number." By "number," we mean any of these things:
You can multiply any of these babies through a matrix with ease.
Say we've got a simple 2 × 2 matrix. Her name is S. We need to find 3S. Here's how that looks:
So 3S is really just 3 multiplied through every entry in the entire 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.