Perron–Frobenius theorem

GPTKB entity

Statements (24)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo non-negative matrices
positive matrices
gptkbp:field linear algebra
matrix theory
https://www.w3.org/2000/01/rdf-schema#label Perron–Frobenius theorem
gptkbp:namedAfter gptkb:Oskar_Perron
gptkb:Georg_Frobenius
gptkbp:publishedIn early 20th century
gptkbp:relatedTo spectral radius
irreducible matrices
primitive matrices
gptkbp:state the largest eigenvalue has an associated positive eigenvector
the largest eigenvalue is positive
a real square matrix with positive entries has a unique largest real eigenvalue
gptkbp:usedIn gptkb:probability_theory
gptkb:Markov_chains
dynamical systems
economics
demography
graph theory
gptkbp:bfsParent gptkb:spectral_graph_theory
gptkb:Oskar_Perron
gptkbp:bfsLayer 6