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All Journal Jurnal Penelitian Fisika dan Aplikasinya (JPFA)
Anggraeni, Sisilia Nur Hikmah Anggraeni
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Astronomy Earth & Planetary Sciences Education Materials Science & Nanotechnology Physics

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Analytic Method And Matrix Diagonalization On Eigen System Of Hermitian Matrix Operator Bambang Supriadi; Anggraeni, Sisilia Nur Hikmah Anggraeni; Badriyah; Fidia Alhikmah Putri; Puput Aprilia Eka Sari; Indah Selviandri; May Yani br Sembiring
Jurnal Penelitian Fisika dan Aplikasinya (JPFA) Vol. 15 No. 1 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jpfa.v15n1.p40-51

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.
Co-Authors Badriyah Bambang Supriadi Fidia Alhikmah Putri Indah Selviandri May Yani br Sembiring Puput Aprilia Eka Sari