The point of an eigenvector is that its direction is stable when you hit it with the given transformation. That is, it&#x27;s an invariant direction of your transformation. This is analogous to the derivative of an exponential function being a simple multiple of that function. It makes it easier to reason about the action of the matrix, and simpler to represent.<p>Imagine I have a matrix transformation that takes a given input vector and converts it into a superposition of a thousand other vectors in random directions; that&#x27;s far harder to reason about than if if just kicked it farther or brought it closer in the same direction.