In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

There are several mathematical theorems named after Ferdinand Georg Frobenius. They include: Frobenius theorem (differential topology) in differential...

Ruelle, or the Perron–Frobenius operator or Ruelle–Perron–Frobenius operator, in reference to the applicability of the Perron–Frobenius theorem to the determination...

be most easily understood as an application of the Perron–Frobenius theorem. This latter theorem comes from a branch of linear algebra known as the theory...

Oskar Perron (7 May 1880 – 22 February 1975) was a German mathematician. He was a professor at the University of Heidelberg from 1914 to 1922 and at the...

In functional analysis, the Krein–Rutman theorem is a generalisation of the Perron–Frobenius theorem to infinite-dimensional Banach spaces. It was proved...

positive real components, representing positive feedback. M-matrix Perron–Frobenius theorem, which shows that any Hurwitz matrix must have at least one negative...

{\displaystyle x^{2}-3x+1} is a Perron number. Perron numbers are named after Oskar Perron; the Perron–Frobenius theorem asserts that, for a real square...

identity matrix. For the non-singularity of A, according to the Perron–Frobenius theorem, it must be the case that s > ρ(B). Also, for a non-singular M-matrix...

positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main diagonal Diagonalizable...

because of the corresponding property for nonnegative matrices. Perron–Frobenius theorem Nonnegative matrices Delay differential equation M-matrix P-matrix...

Hilbert's metric and the Banach contraction principle to rederive the Perron–Frobenius theorem in finite-dimensional linear algebra and its analogues for integral...

refinement of the Gershgorin Circle Theorem. For matrices with non-negative entries, see Perron–Frobenius theorem. Doubly stochastic matrix Hurwitz-stable...

\leq d} nonzero terms. Alternative proofs use Helly's theorem or the Perron–Frobenius theorem. For any nonempty P ⊂ R d {\displaystyle P\subset \mathbb...

Gamas's Theorem (multilinear algebra) Gershgorin circle theorem (matrix theory) Inverse eigenvalues theorem (linear algebra) Perron–Frobenius theorem (matrix...

above by the maximum degree. This can be seen as result of the Perron–Frobenius theorem, but it can be proved easily. Let v be one eigenvector associated...

transitions from one state to some other state of the system. The Perron–Frobenius theorem gives sufficient conditions for a Markov chain to have a unique...

eigenvectors of square positive matrices are described by the Perron–Frobenius theorem. The trace and every row and column sum/product of a nonnegative...

all the entries in the eigenvector be non-negative imply (by the Perron–Frobenius theorem) that only the greatest eigenvalue results in the desired centrality...

Frobenius's theorem (group theory) Frobenius conjecture Frobenius–Schur indicator Perron–Frobenius theorem Quadratic Frobenius test Rouché–Frobenius theorem...

Felix Gantmacher as Kotelyanskiĭ lemma. Diagonally dominant matrix Perron–Frobenius theorem Sylvester's criterion Hawkins, David; Simon, Herbert A. (1949)...

unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure...

{\displaystyle G^{*}} belong to the class of Perron–Frobenius operators and according to the Perron–Frobenius theorem the CheiRank P i ∗ {\displaystyle P_{i}^{*}}...

column vector with all entries equal to 1. This is stated by the Perron–Frobenius theorem. If, by whatever means, lim k → ∞ P k {\textstyle \lim _{k\to \infty...

for which the eigenvalue is unity. Stationary ergodic process Perron–Frobenius theorem Stationary state or ground state in quantum mechanics This set...

problem above, and an active set method called TNT-NN. M-matrix Perron–Frobenius theorem Chen, Donghui; Plemmons, Robert J. (2009). Nonnegativity constraints...

is also a stationary probability vector. On the other hand, the Perron–Frobenius theorem also ensures that every irreducible stochastic matrix has such...

matrices. Normed eigenvectors exist and are unique by the Perron or Perron–Frobenius theorem. Example: consumers and products. The relation weight is the...

multiplicity one. The "only if" direction is a consequence of the Perron–Frobenius theorem. There is also a criterion for regular and connected graphs : a...

diagnosed by Frank H. Hahn.[citation needed] He returned to the Perron–Frobenius theorem with his book The Dynamics of A Capitalist Economy. Goodwin's interest...