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A Brauer’s theorem and related results

Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

A classification of two-peak sincere posets of finite prinjective type and their sincere prinjective representations

Justyna Kosakowska (2001)

Colloquium Mathematicae

Assume that K is an arbitrary field. Let (I, ⪯) be a two-peak poset of finite prinjective type and let KI be the incidence algebra of I. We study sincere posets I and sincere prinjective modules over KI. The complete set of all sincere two-peak posets of finite prinjective type is given in Theorem 3.1. Moreover, for each such poset I, a complete set of representatives of isomorphism classes of sincere indecomposable prinjective modules over KI is presented in Tables 8.1.

Absolutely flat idempotents.

Johnson, Charles R., Harel, Yonatan, Hillar, Christopher J., Groves, Jonathan M., Rault, Patrick X. (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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