# EigenValues and EigenVectors in PCA?

can you please tell me why eigenvalues are used in PCA. Specifically why and how does it explain the variance of the components

To explain coupling, think of two variables, area,$$A$$ and perimeter,$$P$$ of a rectangle. We know that $$A = width * height$$ and $$P = 2(width+height)$$. Thus we can say that $$A$$ and $$p$$ is coupled with $$width$$ and $$height$$ of the rectangle, changing $$A$$ will also change $$p$$ because of the change of $$width$$ and $$height$$. Though the example I given is not linear, you can get the idea.