On solutions of the matrix equation T'AT = A2
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This article is published in Linear Algebra and its Applications.The article was published on 1974-10-01 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Matrix function & Matrix differential equation.read more
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Nonlinear Perron-Frobenius theory
Bas Lemmens,Roger D. Nussbaum +1 more
TL;DR: This is the first comprehensive and unified introduction to nonlinear Perron–Frobenius theory suitable for graduate students and researchers entering the field for the first time and acquaints the reader with recent developments and provides a guide to challenging open problems.
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Invariant metrics, contractions and nonlinear matrix equations
Hosoo Lee,Yongdo Lim +1 more
TL;DR: In this paper, the authors consider the semigroup generated by the self-maps on the open convex cone of positive definite matrices of translations, congruence transformations and matrix inversion that includes symplectic Hamiltonians and show that every member of the semi-group contracts any invariant metric distance inherited from a symmetric gauge function.
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The Cayley-Hilbert metric and positive operators
TL;DR: In this paper, the Cayley-Hilbert metric is defined for a real Banach space containing a closed cone, and the Banach contraction mapping theorem is used to prove the existence of a unique fixed point of the operator with explicit upper and lower bounds.
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Applications of Hilbert's projective metric to a class of positive nonlinear operators
TL;DR: In this article, the authors studied the eigenvalue problems for a class of positive nonlinear operators and established existence, uniqueness and continuity results for positive eigensolutions of a particular type of nonlinear operator.
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Extensions of Jentzsch’s theorem
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An elementary proof of the hopf inequality for positive operators
TL;DR: In this article, Ostrowski et al. established the connection between a theory of BIRXHOFF [1] on positive linear transformations and the theory of HOl'F [3] on the positive linear integral operators.