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

Bambang Supriadi (Universitas Jember)
Sisilia Nur Hikmah Anggraeni Anggraeni (Universitas Jember)
Badriyah (Universitas Jember)
Fidia Alhikmah Putri (Universitas Jember)
Puput Aprilia Eka Sari (Universitas Jember)
Indah Selviandri (Universitas Jember)
May Yani br Sembiring (Universitas Jambi)

Jurnal Penelitian Fisika dan Aplikasinya (JPFA)
Vol. 15 No. 1 (2025)

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.