Eigenvalues

Eigenvalues are numbers that describe how a particular transformation, like stretching or squeezing, affects an entity called an eigenvector. Imagine a process that changes a shape—while most directions might get rotated or reshaped unpredictably, some specific directions only get scaled (enlarged or shrunk) without changing their direction. The eigenvalues quantify this scaling factor along those special directions. In essence, they tell us how much a transformation amplifies or diminishes vectors aligned in particular ways, providing insight into the transformation's core characteristics.