Analytic Method And Matrix Diagonalization On Eigen System Of Hermitian Matrix Operator - Bambang Supriadi; Sisilia Nur Hikmah Anggraeni Anggraeni; Badriyah; Fidia Alhikmah Putri; Puput Aprilia Eka Sari; Indah Selviandri; May Yani br Sembiring (Universitas Negeri Surabaya, 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.