We show that a unitary upper Hessenberg matrix with positive subdiago-nal elements is uniquely determined by its eigenvalues and the eigenvalues of a modiied principal submatrix. This provides an analog of a well-known result for Jacobi matrices.

Karl Gebhardt (1897–1948) had a distinguished career as professor of sports medicine before the Second World War. He developed sports for the disabled at a specialised orthopaedic clinic at Hohenlychen and was President of the Red Cross in Germany. During the war, Gebhardt also acted as Heinrich Himmler’s personal physician and was responsible for medical experimentation on prisoners in the con...

The purpose of this reaserch is to measure the phase equilibrium data of the ternary system (water + phosphoric acid + 1-nonanol) at different temperatures. Experimental solubility curves and tie-line points for the system were obtained at T = 298.2, 308.2 and 318.2 K and ambient pressure. The binodal curve data were detected by the cloud point method. The mass fractions of each layer ...

Karl Popper, though not trained as a physicist and embarrassed early in his career by a physics error pointed out by Einstein and Bohr, ultimately made substantial contributions to the interpretation of quantum mechanics. As was often the case, Popper initially formulated his position by criticizing the views of others—in this case Niels Bohr and Werner Heisenberg. Underlying Popper’s criticism...

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Karl Johan Åström & Richard M. Murray: Feedback Systems is published by Princeton University Press and copyrighted, © 2008, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except f...

We characterize matrices A ∈ Cn×n whose zero/nonzero pattern requires that the controllability matrix [b Ab Ab . . . An−1b] ∈ Cn×n is of full rank, where b ∈ Cn×1 has exactly one nonzero entry. When all the diagonal entries of A are nonzero we show that this occurs if and only if QAQ is unreduced upper Hessenberg, with Q being a permutation matrix for which Qb = [b1, 0, . . . , 0] T . We also c...

In this paper, a class of Hessenberg matrices is presented for adoption as test matrices. The Moore-Penrose inverse and the Drazin inverse for each member of this class are determined explicitly.

In this paper we prove that the simplest band representations of unitary operators on a Hilbert space are five-diagonal. Orthogonal polynomials on the unit circle play an essential role in the development of this result, and also provide a parametrization of such five-diagonal representations which shows specially simple and interesting decomposition and factorization properties. As an applicat...