Ranks of permutative matrices

• Autorzy: Xiaonan Hu , Charles R. Johnson , Caroline E. Davis , Yimeng Zhang
• Języki publikacji: EN

Abstrakty

EN

A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.

Słowa kluczowe

EN

h, k-partition; h, k, g-partition; Identically singular; Latin square; Permutative matrix; Polynomialmatrix; Row grouping

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 233-246

Daty

otrzymano

2015-10-26

zaakceptowano

2016-05-07

online

2016-06-03

Twórcy

autor

Xiaonan Hu

• Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187

autor

Charles R. Johnson

• Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187

autor

Caroline E. Davis

• Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187

autor

Yimeng Zhang

• Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187

Bibliografia

• [1] http//oeis.orgwikiUser:Alexander_Adam#The_rank_of_the_modular_multiplication_table
• [2] J, Dénes and A. D. Keedwell. Latin squares and their applications. New York-London: Academic Press. p. 547. ISBN 0-12- 209350-X. MR 351850, 1974.
• [3] S. Furtado and C. R. Johnson. On the similarity classes among products of m nonsingular matrices in various orders. Linear Algebra Appl., v. 450, p. 217-242, 2014. [WoS]
• [4] C. F. Laywine and G. L. Mullen. Discrete mathematics using Latin squares. Wiley-Interscience Series in Discrete Mathematics and Optimization. New York: John Wiley & Sons, Inc., pp. xviii+305. ISBN 0-471-24064-8. MR 1644242, 1998.
• [5] P. Paparella. Realizing Suleimanova-type Spectra via Permutative Matrices, Electron. J. Linear Algebra, 31, 306-312, 2016. [WoS]
• [6] H. R. Sule˘imanova. Stochasticmatrices with real characteristic numbers. Doklady Akad. Nauk SSSR (N.S.), 66:343-345, 1949.

Identyfikatory

DOI

10.1515/spma-2016-0022