On congruent selection of the Jordan blocks from a singular square matrix
Kh.D. Ikramov
Lomonosov Moscow State University, Moscow, Leninskie Gory, 1, Russia, 119899
Keywords: конгруэнтное преобразование, жорданова клетка, СР-разложение, рациональный алгоритм, congruent transformation, Jordan block, SN-decomposition, rational algorithm
Abstract
The concept of a regularizing decomposition was introduced by R. Horn and V. Sergeichuk. This means the representation of a square matrix by a direct sum of the Jordan blocks with zero on the principal diagonal and a non-singular matrix. Such a representation is attained via congruent transformations and differs from the Jordan normal form. For the reasons explained in this paper, we prefer to speak about the SN-decomposition of a matrix (in other words, singular-non-singular decomposition) rather than the regularizing decomposition. Accordingly, the algorithms providing the former decomposition are called SN-algorithms. We propose a rational algorithm that considerably simplifies the SN-algorithms proposed by Horn and Sergeichuk.
|
