Analytic Method And Matrix Diagonalization On Eigen System Of Hermitian Matrix Operator

Authors

  • Bambang UNIVERSITAS JEMBER
  • Sisilia Nur Hikmah Anggraeni Anggraeni Universitas Jember
  • Badriyah Department of Physics Education, Faculty of Teacher Training and Education, Universitas Jember, Jalan Kalimantan Tegalboto, Jember 68121
  • Fidia Alhikmah Putri Universitas Jember
  • Puput Aprilia Eka Sari Universitas Jember
  • Indah Selviandri Universitas Jember
  • May Yani br Sembiring

DOI:

https://doi.org/10.26740/jpfa.v15n1.p40-51

Keywords:

matrix, eigen system, hermitian operators

Abstract

The solution of the Hermitian eigenoperator matrix problem produces an eigensystem consisting of eigenvalues ​​and eigenvectors. This study aims to determine the complete solution of the eigensystem and the diagonalization of the Hermitian order matrix operator.  analytically. The results of the study show that every eigenproblem in the Hermitian matrix operator  generate several eigenvalues  according to the order of the matrix operator, the eigenvalues ​​are real numbers. Eigenvectors,  of the Hermitian matrix operators are orthogonal because  and   thus forming a basis matrix  and is unitary. A Hermitian matrix can be diagonalized through its basis matrices and a diagonal matrix is ​​obtained.  whose diagonal elements are the eigenvalues ​​of the Hermitian operator.

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Published

2025-06-30

How to Cite

Bambang Supriadi (2025) “Analytic Method And Matrix Diagonalization On Eigen System Of Hermitian Matrix Operator”, Jurnal Penelitian Fisika dan Aplikasinya (JPFA), 15(1), pp. 40–51. doi: 10.26740/jpfa.v15n1.p40-51.

Issue

Vol. 15 No. 1 (2025)

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