Eigenvalues and Eigenvectors for 3×3 Symmetric Matrices:  An Analytical Approach

Abu Bakar Siddique; Tariq A. Khraishi

doi:10.9734/jamcs/2020/v35i730308

Research Article Open access CC BY 4.0

Eigenvalues and Eigenvectors for 3×3 Symmetric Matrices: An Analytical Approach

Abu Bakar Siddique, Tariq A. Khraishi

Journal of Advances in Mathematics and Computer Science · pp. 106–118 · Published 21 Oct 2020

10.9734/jamcs/2020/v35i730308

Abstract

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.

Eigenvalues eigenvectors linear algebra analytical solutions.

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Abu Bakar Siddique, Tariq A. Khraishi (2020). Eigenvalues and Eigenvectors for 3×3 Symmetric Matrices: An Analytical Approach. Journal of Advances in Mathematics and Computer Science , 106–118. https://doi.org/10.9734/jamcs/2020/v35i730308

Affiliations

Abu Bakar Siddique — Department of Mechanical Engineering, University of New Mexico, USA.
Tariq A. Khraishi — Department of Mechanical Engineering, University of New Mexico, USA.

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