Mathematics

New linear algebra study findings have been reported from University of Melbourne

  2008 NOV 10 - (VerticalNews.com) -- "This paper reviews the equations ax = c and xb = d from a new perspective by studying them in the setting of associative rings with or without involution," investigators in Melbourne, Australia report.

  "Results for rectangular matrices and operators between different Banach and Hilbert spaces are obtained by embedding the 'rectangles' into rings of square matrices or rings of operators acting on the same space. Necessary and sufficient conditions using generalized inverses are given for the existence of the Hermitian, skew-Hermitian, reflexive, antireflexive, positive and real-positive solutions, and the general solutions are described in terms of the original elements or operators," wrote A. Dajic and colleagues, University of Melbourne.

  The researchers concluded: "New results are obtained, and many results existing in the literature are recovered and corrected."

  Dajic and colleagues published their study in Linear Algebra and Its Applications (Equations ax = c and xb = d in rings and rings with involution with applications to Hilbert space operators. Linear Algebra and Its Applications, 2008;429(7):1779-1809).

  For additional information, contact J.J. Koliha, University of Melbourne, Dept. of Math & Statistics, Melbourne, Vic 3010, Australia.

  The publisher of the journal Linear Algebra and Its Applications can be contacted at: Elsevier Science Inc., 360 Park Avenue South, New York, NY 10010-1710, USA.

  Keywords: Mathematics, University of Melbourne.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.