Open AccessOn the structure of least common multiple matrices from some class of matrices
Author(s) -
А. М. Романів
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.10.1.179-184
Subject(s) - mathematics , invertible matrix , class (philosophy) , matrix (chemical analysis) , matrix analysis , commutative property , pure mathematics , normal matrix , combinatorics , algebra over a field , eigenvalues and eigenvectors , computer science , materials science , physics , quantum mechanics , artificial intelligence , composite material
For non-singular matrices with some restrictions, we establish the relationships between Smith normal forms and transforming matrices (a invertible matrices that transform the matrix to its Smith normal form) of two matrices with corresponding matrices of their least common right multiple over a commutative principal ideal domains. Thus, for such a class of matrices, given answer to the well-known task of M. Newman. Moreover, for such matrices, received a new method for finding their least common right multiple which is based on the search for its Smith normal form and transforming matrices.