The Group of Quotients of the Semigroup of Invertible Nonnegative Matrices Over Local Rings

2021 ◽  
Vol 257 (6) ◽  
pp. 860-875
Author(s):  
V. V. Nemiro
Keyword(s):  
Local Rings ◽  
Nonnegative Matrices

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

scholarly journals The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Antoine Gautier ◽  
Matthias Hein ◽  
Francesco Tudisco
Keyword(s):  
Global Convergence ◽  
Convergence Theorem ◽  
Matrix Norm ◽  
Nonnegative Matrices ◽  
Np Hard ◽  
Power Method ◽  
Contraction Ratio ◽  
Matrix Norms ◽  
Vector Norms

AbstractWe analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $$\ell ^p$$ ℓ p matrix norms. In particular, exploiting the Birkoff–Hopf contraction ratio of nonnegative matrices, we obtain novel and explicit global convergence guarantees for a range of matrix norms whose computation has been recently proven to be NP-hard in the general case, including the case of mixed-subordinate norms induced by the vector norms made by the sum of different $$\ell ^p$$ ℓ p -norms of subsets of entries.

scholarly journals On the similarity to nonnegative and Metzler Hessenberg forms

2021 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Christian Grussler ◽  
Anders Rantzer
Keyword(s):  
Standard Form ◽  
Complete Characterization ◽  
Nonnegative Matrices ◽  
Positive Systems ◽  
Third Order ◽  
Hessenberg Form ◽  
Hessenberg Matrices ◽  
Open Question ◽  
Order Continuous

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

scholarly journals Analytic ramifications and flat couples of local rings

1981 ◽  
Vol 146 (0) ◽  
pp. 201-208 ◽  
Author(s):  
Tomas Larfeldt ◽  
Christer Lech
Keyword(s):  
Local Rings

scholarly journals Characterizations of regular local rings via syzygy modules of the residue field

2018 ◽  
Vol 10 (3) ◽  
pp. 327-337
Author(s):  
Dipankar Ghosh ◽  
Anjan Gupta ◽  
Tony J. Puthenpurakal
Keyword(s):  
Residue Field ◽  
Local Rings ◽  
Syzygy Modules ◽  
Regular Local Rings

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

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