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All Journal Jurnal Penelitian Fisika dan Aplikasinya (JPFA) Jurnal Pendidikan Fisika Indonesia
Fidia Alhikmah Putri
Universitas Jember
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; Sisilia Nur Hikmah Anggraeni 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.
The Effectiveness of Special Relativity Student Worksheet Assisted by The Pythagorean Theorem in Physics Learning Bambang Supriadi; Sakti Kalisa Sefanda; Badriyah Badriyah; Fidia Alhikmah Putri; Ummi Zahrotul Ainiyah; Habibah Khusna Baihaq; Muhammad Najih Hamdi
Jurnal Pendidikan Fisika Indonesia Vol. 22 No. 1 (2026)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/jpfi.v22i1.37661

Abstract

In the 21st-century education era, integrating innovative learning media is essential to develop mathematical thinking skills and improve overall student learning outcomes, especially when addressing highly abstract physics topics such as Einstein’s special theory of relativity. This research aims to implement a specifically designed Student Worksheet (SW) assisted by the Pythagoras theorem to develop mathematical thinking indicators, enhance student learning performance, and evaluate student responses toward the media. The research employed a pre-experimental method with a one-group pretest-posttest design conducted at SMAN Mumbulsari during the 2024/2025 academic year. Using convenience sampling, 72 eleventh-grade students from two physics elective classes were selected as research subjects. Data collection was carried out using validated pretest-posttest essay questions, Student Worksheets focused on four key mathematical thinking elements: specializing, generalizing, conjecturing, and convincing, and response questionnaires based on a Likert scale. Data analysis utilized the Normalized Gain (N-gain) score to measure the improvement in learning outcomes and descriptive statistics to determine the percentage of student responses. The results indicated that students' mathematical thinking skills fell into the good to very good range across all indicators. Furthermore, learning outcomes showed an average N-gain of 0.57, placing the improvement in the moderate category, complemented by a positive student response rate of 68.20%. These findings demonstrate that the Pythagoras-assisted SW effectively improves learning performance in physics. This research provides significant practical benefits as an innovative instructional alternative for physics teachers, simplifying complex, abstract concepts through a geometric approach, thereby helping students overcome mathematical barriers and fostering a deeper understanding of physics.
Co-Authors Badriyah Badriyah Badriyah Bambang Supriadi Habibah Khusna Baihaq Indah Selviandri May Yani br Sembiring Muhammad Najih Hamdi Puput Aprilia Eka Sari Sakti Kalisa Sefanda Sisilia Nur Hikmah Anggraeni Anggraeni Ummi Zahrotul Ainiyah