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Rational G-Circulants Satisfying the Matrix Equation A² = dI + λJ

Citation

Lam, Clement Wing Hong (1974) Rational G-Circulants Satisfying the Matrix Equation A² = dI + λJ. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7qh9-nn17. https://resolver.caltech.edu/CaltechTHESIS:02022021-194446003

Abstract

A g-circulant is a square matrix of rational numbers in which each row is obtained from the preceding row by shifting the elements cyclically g columns to the right. This work studies g-circulants A which satisfy the matrix equation A2 = dI + λJ, where I is the identity matrix and J is the matrix of 1's. Necessary and sufficient conditions are given for the existence of solutions when g = 1. The existence of (0,1) g-circulants satisfying A2 = dI + λJ is shown to be equivalent to the existence of (v, k, λ, g)-addition sets, which are generalizations of difference sets. It is proved that there are no nontrivial (v, k, λ, 1)-addition sets. Some examples of (v, k, λ, g)-addition sets are given and the multiplier theorem for (v, k, λ, g)-addition sets is also proved.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics; Engineering Science
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ryser, Herbert J. (advisor)
  • Kisilevsky, Hershey Harry (co-advisor)
  • Taussky-Todd, Olga (co-advisor)
Thesis Committee:
  • Ryser, Herbert J.
  • Kisilevsky, Hershey Harry
  • Taussky-Todd, Olga
Defense Date:5 March 1974
Funders:
Funding AgencyGrant Number
CaltechUNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Record Number:CaltechTHESIS:02022021-194446003
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:02022021-194446003
DOI:10.7907/7qh9-nn17
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14071
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:04 Feb 2021 17:16
Last Modified:04 Feb 2021 21:47

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