Proceedings of the American Mathematical Society

Author(s): Dragomir Z. Ðokovic; Fernando Szechtman
Journal: Proc. Amer. Math. Soc. 133 (2005), 2853-2863.
MSC (2000): Primary 15A63
Posted: March 29, 2005
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Abstract: We study finite-dimensional bilinear spaces and their isometry groups. To each bilinear space

we associate two canonical filtrations, which yield structural results on

. Prominent among these is an explicit formula for the number of indecomposable and degenerate blocks of

of a given dimension. Equipped with this material, we proceed to characterize those bilinear spaces whose isometry group is contained in the special linear group. This characterization can easily be implemented in practice by means of an algorithm. As an application, we determine the real

-by-

matrices whose congruence class is disconnected.

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Dragomir Z. Ðokovic
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: djokovic@uwaterloo.ca

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