Open AccessEigenvalues and Eigenvectors for 3×3 Symmetric Matrices: An Analytical Approach
Author(s) -
Abu Bakr Siddique,
Tariq Khraishi
Publication year - 2020
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2020/v35i730308
Subject(s) - eigenvalues and eigenvectors , matrix differential equation , modal matrix , mathematics , eigenvalue perturbation , defective matrix , matrix (chemical analysis) , symmetric matrix , eigenvalues and eigenvectors of the second derivative , spectrum of a matrix , numerical analysis , dimension (graph theory) , mathematical analysis , diagonalizable matrix , pure mathematics , physics , differential equation , materials science , quantum mechanics , composite material
Research problems are often modeled using sets of linear equations and presented as matrix equations. Eigenvalues and eigenvectors of those coupling matrices provide vital information about the dynamics/flow of the problems and so needs to be calculated accurately. Analytical solutions are advantageous over numerical solutions because numerical solutions are approximate in nature, whereas analytical solutions are exact. In many engineering problems, the dimension of the problem matrix is 3 and the matrix is symmetric. In this paper, the theory behind finding eigenvalues and eigenvectors for order 3×3 symmetric matrices is presented. This is followed by the development of analytical solutions for the eigenvalues and eigenvectors, depending on patterns of the sparsity of the matrix. The developed solutions are tested against some examples with numerical solutions.