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On eigenvalues of meet and join matrices associated with incidence functions
Abstract Let ( P , ⪯ , ∧ ) be a locally finite meet semilattice. Let S = { x 1 , x 2 , … , x n } , x i ⪯ x j ⇒ i ⩽ j , be a finite subset of P and let f be a complex-valued function on P . Then the nExpand
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Inequalities for spreads of matrix sums and products.
Let A and B be complex matrices of same dimension. Given their eigen- values and singular values, we survey and further develop simple inequalities for eigenvalues and singular values of A + B, AB ,aExpand
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A best upper bound for the 2-norm condition number of a matrix
Abstract Let A be an n × n nonsingular real or complex matrix. The best possible upper bound for the ratio of the largest and smallest singular values of A, using tr A∗A , det A, and n only, isExpand
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Bounds for Eigenvalues Using the Trace and Determinant
Abstract Let A be a square matrix with real and positive eigenvalues λ 1 ⩾ … ⩾ λ n > 0, and let 1 ≤ k ≤ l ≤ n . Bounds for λ kl … λ l and λ k + … + λ l , involving k, l, n, tr A , and det A only, areExpand
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Mathematical Modelling
TLDR
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Expand
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ON THE STAR PARTIAL ORDERING OF NORMAL MATRICES
We order the space of complex n× n matrices by the star partial ordering ≤∗. So A ≤∗ B means that A∗A = A∗B andAA∗ = BA∗. We find several characterizations for A ≤∗ B in the case of normal matrices.Expand
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Characterizations and lower bounds for the spread of a normal matrix
Abstract The spread of an n×n matrix A with eigenvalues λ1,…,λn is defined by spr A = max j,k |λ j −λ k |. We prove that if A is normal, then spr A = max | x * Ax − y * Ay | | x , y ∈ C n ,∥ x ∥=∥ yExpand
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THE STABILIZING PROPERTIES OF NONNEGATIVITY CONSTRAINTS IN LEAST-SQUARES IMAGE RECONSTRUCTION
The incorporation of nonnegativity constraints in image reconstruction problems is known to have a stabilizing effect on solution methods. In this paper, we both demonstrate and provide anExpand
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Bounds for singular values using traces
Abstract Bounds for the singular values, ratios of singular values, and rank of a square matrix A , involving tr A , tr A 2 , and tr A H A , are presented. Some of the results are analogous to theExpand
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A simple proof for the inequality between the perron root of a nonnegative matrix and that of its geometric symmetrization
AbstractLet A = (aij) be a nonnegative square matrix, let G = (gij) be its geometric symmetrization, i.e., gij = $$ \sqrt {a_{ij} a_{ji} } $$, and let ρ denote the Perron root. We present a simpleExpand
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