Reachability matrices and cyclic matrices

Reachability matrices and cyclic matrices

Ela Reachability Matrices and Cyclic Matrices

Received by the editors September 23, 2009. Accepted for publication February 11, 2010. Handling Editor: Daniel Szyld. Dipartimento di Ingegneria dell’Informazione, Università di Padova, I-35131 Padova, Italy ([email protected]). Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany ([email protected]). Electronic Journal of Linear Algebra ISSN 1081-3810 A...

E-Clean Matrices and Unit-Regular Matrices

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

The Reachability Cones of Essentially Nonnegative Matrices

Let A be an n× n essentially nonnegative matrix and consider the linear differential system ẋ(t) = Ax(t), t ≥ 0. We show that there exists a constant h(A) > 0 such that the trajectory emanating from xo reaches R + at a finite time to = t(xo) ≥ 0 if and only if the sequence of points generated by a finite differences approximation from xo, with time–step 0 < h < h(A), reaches R + at a finite ind...

Cyclic Monodromy Matrices for Sl(n) Trigonometric R-matrices

The algebra of monodromy matrices for sl(n) trigonometric R-matrix is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators. Cocommutativity of representations is discussed and inter-twiners for factorizable representations are written through the Boltzmann weights of the sl(n) chiral Potts m...