Determination of eigenvectors with Lagrange multipliers

Wooyong Han, Dong Won Jung, Jungil Lee, Chaehyun Yu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We present a method to determine the eigenvectors of an n× 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.

Original languageEnglish
Pages (from-to)1018-1022
Number of pages5
JournalJournal of the Korean Physical Society
Issue number11
Publication statusPublished - 2021 Jun

Bibliographical note

Funding Information:
As members of the Korea Pragmatist Organization for Physics Education (KPOP), the authors thank the remaining members of KPOP for useful discussions. This work is supported in part by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) under Contract Nos. NRF-2020R1A2C3009918 (JL), NRF-2017R1E1A1A01074699 (JL), and NRF-2018R1D1A1B07047812 (DWJ). The work of CY is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1I1A1A01073770).

Publisher Copyright:
© 2021, The Korean Physical Society.


  • Diagonalization
  • Eigenvalue problem
  • Eigenvector
  • Gauge fixing
  • Hermitian matrix
  • Lagrange multiplier

ASJC Scopus subject areas

  • General Physics and Astronomy


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