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Volume 36, Number 4, pages 409-416 (2025)
https://doi.org/10.26830/symmetry_2025_4_409
VISUALIZING SYMMETRIC MATRICES IN A CAS-ASSISTED LEARNING ENVIRONMENT USING MATLAB
Günhan Caglayan
New Jersey City University, NJ 07305. U.S.A.
Email: gcaglayan@njcu.edu
Abstract: This paper explores the visualization of symmetric and Hermitian matrices with distinct eigenvalues in a MATLAB-assisted computer algebra system (CAS) learning environment. Focusing on real symmetric matrices and complex Hermitian matrices, the study illustrates how eigenvalues and eigenvectors can be computed and visualized to verify key theoretical results, such as the spectral theorem. Using MATLAB, we demonstrate orthogonal and unitary diagonalization for symmetric and Hermitian matrices, respectively, and confirm the orthogonality of eigenvectors associated with distinct eigenvalues. A series of examples, including 4×4 and 3×3 real symmetric matrices, a 2×2 Hermitian matrix, and a 5×5 Householder matrix, highlight how computational tools can transform abstract linear algebra concepts into intuitive visual experiences.
Keywords: symmetric and Hermitian matrices, MATLAB, CAS, pedagogy of l. algebra.
References:
Attaway, S. (2022) MATLAB: A Practical Introduction to Programming and Problem Solving (6th ed.), Elsevier.
Householder, A. S. (1953) Principles of Numerical Analysis. New York: McGraw-Hill, pp. 135-138.
Trefethen, L. N., & Bau, D. (1997) Numerical Linear Algebra, SIAM. https://doi.org/10.1137/1.9780898719574
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