At the heart of image manipulation are special matrices that can be used to create effects. You can use these effects separately or combine them for more complex operations. They are the heart of linear algebra itself.
Linear algebra is the math of shaped collections of numbers.
The mathematics we are most familiar with deals with numbers called scalars. Each of these values is a magnitude of some quantity that interests us. Often we use combinations of values to represent more complex information. Your speed cannot be negative, but your velocity could be. Think about your car moving in reverse.