In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

we give further results for perron-frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. we indicate two techniques for establishing the main theorem ofperron and frobenius on the numerical range. in the rst method, we use acorresponding version of wielandt's lemma. the second technique involves graphtheory.

The Perron–Frobenius theorem plays an important role in many areas of management science and operations research. This article provides a probabilistic perspective on the theorem, by discussing proof that exploits representation eigenvalue eigenvectors terms dynamics Markov chain. recovers conditions both finite-dimensional infinite-dimensional settings under which have been shown to exist othe...

Given a manifold M of dimension n + k, attach to every p ∈ M an ndimensional subspace of the tangent space Tp(M). It is natural to ask if this collection of subspaces is the collection of tangent spaces to a family of submanifolds that cover M . In this paper we prove Frobenius’ Theorem, which gives a necessary and sufficient condition for the answer to be yes.

The representation theory of finite groups began with Frobenius's factorization Dedekind's group determinant. In this paper, we consider the case semigroup determinant is nonzero if and only complex algebra Frobenius, so our results include applications to study Frobenius algebras. We explicitly factor for commutative semigroups inverse semigroups. recover Wilf-Lindström a meet semilattice Wood...

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assur...

The quantum general linear supergroup GL q (m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of GL q (m|n). Quantum Frobenius reciprocity is proven, and a Borel-Weil theorem is established for the covariant and contravariant tensor irreps.

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.