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Mathematics

The Power Method for Approximating Dominant Eigenvalues

Quick fact

The power method can compute the dominant eigenvalue of a matrix with millions of entries (like the web graph in Google's PageRank) using only repeated matrix-vector multiplications, which can be done efficiently even on huge sparse matrices.

Why this is interesting

Imagine you have a huge matrix that describes connections between web pages, and you need to know which page is most important. How can you find the dominant eigenvalue without performing expensive calculations?