M-matrices: a generalization of M-matrices based on eventually nonnegative matrices.
Majorants of matrix norms and spectrum localization
Maps on matrices that preserve the spectral radius distance
Let ϕ be a surjective map on the space of n×n complex matrices such that r(ϕ(A)-ϕ(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that ϕ must be a composition of five types of maps: translation, multiplication by a scalar of modulus one, complex conjugation, taking transpose and (simultaneous) similarity. In particular, ϕ is real linear up to a translation.
Maps preserving spectral radius, numerical radius, spectral norm.
Matrices totally positive relative to a tree.
Matrices with Prescribed Characteristic Polynomial and a Prescribed Submatrix III.
Matrices with prescribed characteristic polynomial and submatrices
Matrix functions preserving sets of generalized nonnegative matrices.
Matrix rank/inertia formulas for least-squares solutions with statistical applications
Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function Φ(Z) = Q − ZPZ0 is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this paper, we establish a group of formulas for calculating maximum and minimum ranks and inertias of Φ(Z)...
Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.
Minimum rank of a tree over an arbitrary field.
Minimum semidefinite rank of outerplanar graphs and the tree cover number.
Modelling the Spread of Infectious Diseases in Complex Metapopulations
Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially,...
Modification of the - factorization method for multiparameter polynomial matrices and their properties.
Monomorphisms in spaces with Lindelöf filters
is the category of spaces with filters: an object is a pair , a compact Hausdorff space and a filter of dense open subsets of . A morphism is a continuous function for which whenever . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically address only one of these...
Monotone interval eigenproblem in max–min algebra
The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.
More counterexamples to the Alon-Saks-Seymour and rank-coloring conjectures.
Multiplicative maps on invertible matrices that preserve matricial properties.