Perron–Frobenius Theory
Spectra of nonnegative matrices and Markov chain applications.
Perron–Frobenius Theory. Spectra of nonnegative matrices and Markov chain applications. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of perron–frobenius theory approach the subject from complementary angles. Berman, Nonnegative Matrices in the Mathematical Sciences (1994) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Horn, Matrix Analysis (2013) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for perron–frobenius theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1994Nonnegative Matrices in the Mathematical Sciencesberman-1994, plemmons-1994
- textbook · primary · 2013Matrix Analysishorn-2013, johnson-2013
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