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Applications of Perron–Frobenius theory to population dynamics
Abstract. By the use of Perron–Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in
Linear Preserver Problems
TLDR
This article describes some techniques, outlines a few proofs, and discusses some exceptional results of linear preserver problems, an active research area in matrix and operator theory.
Numerical Range of Matrix Polynomials
Let $M_n$ be the algebra of all $n\times n$ complex matrices. Suppose $$ P(\lambda) = A_m \lambda^m + A_{m-1} \lambda^{m-1} + \cdots + A_0 $$ is a matrix polynomial, where $A_i \in M_n$ and $\lambda$
The Lidskii-Mirsky-Wielandt theorem – additive and multiplicative versions
TLDR
A simple matrix splitting technique is used to give an elementary new proof of the Lidskii-Mirsky-Wielandt Theorem and to obtain a multiplicative analog of it, which is argued is the fundamental bound in the study of relative perturbation theory for eigenvalues of Hermitian matrices and singular values of general matrices.
MATRICES WITH CIRCULAR SYMMETRY ON THEIR UNITARY ORBITS AND C-NUMERICAL RANGES
We give equivalent characterizations for those n x n complex ma- trices A whose unitary orbits %?(A) and C-numerical ranges WC{A) satisfy ei8&(A) = f/(A) or e'e WC(A) = WC(A) for some real 0 (or for
PRESERVERS OF MATRIX PAIRS WITH A FIXED INNER PRODUCT VALUE
Let V be the set of n×n hermitian matrices, the set of n×n symmetric matrices, the set of all effects, or the set of all projections of rank one. Let c be a real number. We characterize bijective
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