Eigenvalue perturbation

Eigenvalue perturbation is a way to figure out how a small change to something will affect the result. To help explain it, let's use an example. Imagine you have a room with eight doors, each numbered 1 through 8. Each door has a different key that triggers a switch that will open the door. Each key has a different size and shape, so it can only fit in one door. Now if you make a small change to the shape or size of one of those keys, that means the key might not fit in the same door anymore. Eigenvalue perturbation is the idea of figuring out which door the key would fit in if it had been made slightly differently. This way, you can understand how even a small change can lead to big results.