Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Localization of the zeros of the permanent of a characteristic matrix


Author: P. M. Gibson
Journal: Proc. Amer. Math. Soc. 31 (1972), 18-20
DOI: https://doi.org/10.1090/S0002-9939-1972-0291184-X
MathSciNet review: 0291184
Full-text PDF

Abstract | References | Additional Information

Abstract: It is shown that many bounds for the eigenvalues of a complex matrix $ A$ are also bounds for the zeros of the permanent of the characteristic matrix of $ A$.


References [Enhancements On Off] (What's this?)

  • [1] J. L. Brenner, Relations among the minors of a matrix with dominant principal diagonal, Duke Math. J. 26 (1959), 563-567. MR 22 #1590. MR 0110722 (22:1590)
  • [2] -, Geršgorin theorems, regularity theorems, and bounds for determinants of partitioned matrices, SIAM J. Appl. Math. 19 (1970), 443-450. MR 0268198 (42:3097)
  • [3] J. L. Brenner and R. A. Brualdi, Eigenschaften der Permanentefunktion, Arch. Math. (Basel) 18 (1967), 585-586. MR 36 #3795. MR 0220743 (36:3795)
  • [4] P. Camion and A. J. Hoffman, On the nonsingularity of complex matrices, Pacific J. Math. 17 (1966), 211-214. MR 33 #129. MR 0191902 (33:129)
  • [5] M. Marcus and H. Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass., 1964. MR 29 #112. MR 0162808 (29:112)
  • [6] A. Ostrowski, Über das Nichtverschwinden einer Klasse von Determinanten und die Lokalisierung der charakteristischen Wurzeln von Matrizen, Compositio Math. 9 (1951), 209-226. MR 13, 524. MR 0045081 (13:524b)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291184-X
Keywords: Permanents, determinants, dominant diagonal matrices, bounds for eigenvalues, spectral radius, nonnegative matrices
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society