Page 58 - Textos de Matemática Vol. 39
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48 RAFAEL CANTO´ AND CHARLES R. JOHNSON
Thus, mr(P) ≤ 5 (in fact, = 5). Thus, the null space upper bounds of [2] do not generally give equality for mr (not noted in [2]).
References
[1] F.R. Gantmacher, The Theory of Matrices, Volume 1, Chelsea Publishing Company, New York (1960).
[2] C.R. Johnson, Y. Zhang, On the possible ranks among matrices with a given pattern, submitted.
Departament de Matema`tica Aplicada Universitat Polit`ecnica de Val`encia 46071 Val`encia, Spain
E-mail address: rcanto@mat.upv.es
Department of Mathematics College of William and Mary Williamsburg
VA 23187-8795, USA
E-mail address: crjohnso@math.wm.edu
