New approach to finding eigenvectors for repeated eigenvalues of a matrix

• 发表在: Sistemnì Doslìdženâ ta Informacìjnì Tehnologìï
• 主要作者: Anatolii Petrenko
• 格式: 文件
• 语言: 乌克兰语
• 出版: Igor Sikorsky Kyiv Polytechnic Institute 2024-12-01
• 主题: 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
• 在线阅读: http://journal.iasa.kpi.ua/article/view/322526
• ISSN: 1681-6048; 2308-8893

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.