FINDING THE ROOTS OF THE CHARACTERISTIC EQUATION OF AN ARBITRARY THREE-DIMENSIONAL SYMMETRIC MATRIX
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Abstract
The procedure for reducing the three-dimensional problem of finding the eigenvectors of the matrix to the two-dimensional case is justified. Disclosed is an algorithm for finding roots of a cubic equation based on transformation of elements of a three-dimensional matrix during rotation of a coordinate system. It is shown that the symmetry of the original matrix can be used as a criterion for the reality of the roots of the equation, which allows us to correlate the invariants of the matrix with the coefficients of the solved equation by appropriate selection of matrix elements.
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References
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