Open AccessThe base matrix of hermitian operator order n<4
Author(s) -
Sindi Epiningtiyas,
Bambang Supriadi,
Trapsilo Prihandono,
B H Saputra,
Muhamad Sukron Makmun,
B H Antono
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1538/1/012048
Subject(s) - hermitian matrix , eigenvalues and eigenvectors , mathematics , diagonal matrix , matrix (chemical analysis) , operator (biology) , square matrix , matrix function , diagonal , mathematical analysis , pure mathematics , symmetric matrix , physics , quantum mechanics , geometry , biochemistry , materials science , chemistry , repressor , transcription factor , composite material , gene
The Eigen problem is a problem that exists when there is an operator that is affected by the function, then that function does not change except being multipled by the constant in the form of an eigenvalue. In general, the eigenvalue problem uses the Hermitian operators by using observable variable in the form of mathematical operations. Hermitian operator is an operator that happens when the Hermit conjugation is performed, then the operator will return to its original condition. This research aims to determine the base matrix of Hermitian operators with order n ≤ 4 (size 2 × 2, 3 × 3 and 4 × 4). Entry element of the hermitian matrix operator uses complex numbers of which each order consists of few Hermitian operators. The method used is an analytical method by inserting problems into the eigen equation then normalized to obtain a diagonal matrix, so as to obtain a complete solution of the eigen problem on form of a matrix (including eigenvalues, normalized eigenvectors, and base matrix). Base matrix that has been obtained will be a diagonal matrix with diagonal elements of the eigenvalue. The results of this research indicate that the base matrix obtained in each order forms a square matrix that has entry elements in the form of complex numbers.