Abstract
This chapter describes the evaluation of eigenvalues and eigenvectors of matrices. Many problems in mechanics and physics entail finding eigenvalues and eigenvectors values of λ for which there are nontrivial solutions of a uniform set of linear algebraic equations. Numerous methods have been evolved to facilitate the expansion of determinant. There are also methods of finding the eigenvalues and eigenvectors without expanding determinant. The first row of the determinant is multiplied by λ to the second row. The first two rows of the new determinant will be the same as for D1(λ). Among the polynomials, there is one polynomial ψ(λ) of least degree with a leading coefficient of 1. In linear algebra, this polynomial is called the reduced characteristic polynomial or minimal polynomial.
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