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Mathematics

The Power Method for Computing Eigenvalues and Eigenvectors

Quick fact

The power method can compute the dominant eigenvalue of a matrix with just a few lines of code, yet it's the engine behind Google's original PageRank algorithm, which ranks web pages by iteratively multiplying a vector by a link matrix.

Why this is interesting

Ever wondered how Google ranks billions of web pages in an instant? Or how engineers predict whether a bridge will collapse? Both rely on a surprisingly simple trick: repeatedly multiplying a vector by a matrix until it settles into a pattern.