Determination of eigenvectors with Lagrange multipliers
- Authors
- Han, Wooyong; Jung, Dong-Won; Lee, Jungil; Yu, Chaehyun
- Issue Date
- 6월-2021
- Publisher
- KOREAN PHYSICAL SOC
- Keywords
- Eigenvalue problem; Eigenvector; Lagrange multiplier; Hermitian matrix; Diagonalization; Gauge fixing
- Citation
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY, v.78, no.11, pp.1018 - 1022
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY
- Volume
- 78
- Number
- 11
- Start Page
- 1018
- End Page
- 1022
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/127950
- DOI
- 10.1007/s40042-021-00112-3
- ISSN
- 0374-4884
- Abstract
- We present a method to determine the eigenvectors of an n x n Hermitian matrix by introducing Lagrange undetermined multipliers. In contrast to a usual Lagrange multiplier that is a number, we introduce matrix-valued multipliers with a constraint equation, which make the eigenvalue equation directly solvable. Then, there exists a unique solution for each eigenvalue equation and the eigenvectors are obtained by imposing the constraint limit. This method is in clear contrast to the conventional approach of Gaussian elimination and it will be a good pedagogical example for conceptual understanding for the gauge symmetry just with the knowledge of quantum physics and linear algebra at the undergraduate level.
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