Construction of 4×4 symmetric stochastic matrices with given spectra
- 주제(키워드) nonnegative inverse eigenvalue problem , symmetric matrices , symmetric stochastic matrices , symmetric stochastic inverse eigenvalue problem
- 발행기관 고려대학교 대학원
- 지도교수 김동균
- 발행년도 2024
- 학위수여년월 2024. 8
- 학위명 박사
- 학과 및 전공 대학원 수학과
- 세부전공 대수학 및 수론전공
- 원문페이지 22 p
- 실제URI http://www.dcollection.net/handler/korea/000000287568
- UCI I804:11009-000000287568
- DOI 10.23186/korea.000000287568.11009.0001561
- 본문언어 영어
초록/요약
The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. When the cardinality of a list is 4, Kaddoura and Mourad provided a sufficient condition for SSIEP by a mapping and convexity technique. They also conjectured that the sufficient condition is the necessary condition. This paper presents the same sufficient condition for SSIEP, but we do it in terms of the list elements. In this way, we provide a different but more straightforward construction of symmetric stochastic matrices for SSIEP compared to those of Kaddoura and Mourad.
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Table of Contents
Abstract i
Acknowledgment ii
Table of Contents iii
1 Introduction 1
2 Symmetric Stochastic Matrices 3
3 Symmetric and Symmetric Stochastic Matrices 12
References 15
