New approach to finding eigenvectors for repeated eigenvalues of a matrix
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2024.4.09Keywords:
eigenvectors, multiples of eigenvalues, algebraic and geometric multiplicity, solutions of degenerate systems, change of spectrum of a matrix, defective and non-defective multiples of a matrixAbstract
An efficient method of calculating eigenvectors for multiple eigenvalues of a matrix is proposed. This method is based on a formalized transformation of the problem of solving degenerate systems of equations into a regular problem by “repairing” their matrices and correspondingly correcting the right-hand sides of the equations, as well as “exclusion” during calculations from the spectrum eigenvalues of the matrix of one of the multiple values. In the case of non-defective multiples of the matrix, orthogonal eigenvectors are formed in contrast to the results obtained using the Mathematica program.
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