New approach to finding eigenvectors for repeated eigenvalues of a matrix

Abstract

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.

Keywords

• 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 matrix