Counting zero kernel pairs over a finite field

Ram, Samrith (2016) Counting zero kernel pairs over a finite field. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 495 . pp. 1-10.

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Abstract

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	LINEAR ALGEBRA AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Keywords:	Zero kernel pair; Matrix completion; Reachable pair; Observable pair; Unimodular matrix polynomial; Finite field
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	23 Apr 2016 05:13
Last Modified:	23 Apr 2016 05:13
URI:	http://eprints.iisc.ac.in/id/eprint/53672

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