Rank According to Perron: A New Insight

by Thomas L. Saaty (University of Pittsburgh)

Mathematics Magazine
October, 1987

Subject classification(s): Eigenvalues and Eigenvectors | Mathematics for Humanities | Data Representation
Applicable Course(s): 3.8 Linear/Matrix Algebra | 7.10 Survey Design & Analysis

Suppose we have several alternatives that we wish to rank.  For example, we may wish to rank five teachers according to their teaching excellence.  The author constructs a positive matrix $$A$$ based on pairwise comparisons of the alternatives, and uses the Perron principal eigenvector to find a ranking.  The author employs dominance walks to obtain these results.

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Capsule Course Topic(s):
Linear Algebra | Application: Markov