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The kernel of the
matrix $\lbrack i\mskip-2mu j \pmod n\rbrack$ when $n$ is
prime
Maria I. Bueno, Susana Furtado, Jennifer Karkoska, Kyanne Mayfield, Robert Samalis and Adam Telatovich
Vol. 9 (2016), No. 2, 265–280
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Abstract |
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In this paper, we consider the matrix whose -th entry is and compute its rank and a basis for its kernel (viewed as a matrix over the real numbers) when is prime. We also give a conjecture on the rank of this matrix when is not prime and give a set of vectors in its kernel, which is a basis if the conjecture is true. Finally, we include an application of this problem to number theory. |
Keywords
rank of a matrix, kernel of a matrix, bisymmetric matrix.
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Mathematical Subject Classification 2010
Primary: 15A03, 11M06, 11M20
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Milestones
Received: 14 October 2014
Revised: 13 April 2015
Accepted: 16 April 2015
Published: 2 March 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Maria I. Bueno | |
| Mathematics Department and College
of Creative Studies The University of California, Santa Barbara Santa Barbara, CA 93106-3080 United States |
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| Susana Furtado | |
| CEAFEL Faculdade de Economia Universidade do Porto 4200-464 Porto Portugal |
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| Jennifer Karkoska | |
| Applied Mathematics Department Rensselaer Polytechnic Institute Troy, NY 12180 United States |
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| Kyanne Mayfield | |
| Fast Enterprises LLC Madison, WI 53704 United States |
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| Robert Samalis | |
| Department of Mathematics University of Georgia Athens, GA 30602 United States |
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| Adam Telatovich | |
| Department of Mathematics Pennsylvania State University State College, PA 16803 United States |
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