eigenvector

An eigenvector of.a square matrix is a vector which when multiplied by the matrix ends up as a multiple of itself. In otherwords, the eigenvector is unchanged except for scale. Mathentaically, if M is the matrix and v an eignevector, Mv = λv. The scale factor λ is known as the eigenvalue of the eigenvector. Eignevectors have many uses, both directly represented within algorithsm, or as a way to epxlian other processes. As an an example of the former, if a cross-correlation matrix is calclated for a dataset, and the eigenvectors with large eigenvalues computed, these correspond to the directions in which the data has greatest variation, a process called principle components analysis. As an example of the altter, Google PageRank agorithm chaxcses link spreading a measure of importance form page to page, however this effectively computes the principal eigenvector (the one with largest {[eigenvalue}}) of the web graph represented as a connection matrix.