Perron–frobenius Theorem for Nonnegative Tensors
نویسندگان
چکیده
We generalize the Perron–Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.
منابع مشابه
The Sign-Real Spectral Radius for Real Tensors
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.
متن کاملPERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES
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.
متن کاملSome results on the block numerical range
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.
متن کاملA unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps
Inspired by the definition of symmetric decomposition, we introduce the concept of shape partition of a tensor and formulate a general tensor spectral problem that includes all the relevant spectral problems as special cases. We formulate irreducibility and symmetry properties of a nonnegative tensor T in terms of the associated shape partition. We recast the spectral problem for T as a fixed p...
متن کاملA Necessary and Sufficient Condition for Existence of a Positive Perron Vector
In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to irreducible nonnegative tensors and weakly irreducible nonnegative tensors recently. This result is a fundamental result in matrix theory and has found wide applications in ...
متن کامل