## 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 A^{2} = 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 A^{2} = 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.)) | ||||||
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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)
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Thesis Committee: | - Ryser, Herbert J.
- Kisilevsky, Hershey Harry
- Taussky-Todd, Olga
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Defense Date: | 5 March 1974 | ||||||

Funders: |
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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: | 07 Jun 2023 17:45 |

## Thesis Files

PDF
- Final Version
See Usage Policy. 11MB |

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