Open AccessRelations Between Ranks of Matrix Polynomials
Author(s) -
V. Topor Pop,
AUTHOR_ID
Publication year - 2021
Publication title -
journal of algebra, number theory : advances and applications
Language(s) - English
Resource type - Journals
ISSN - 0975-1548
DOI - 10.18642/jantaa_7100122167
Subject(s) - rank (graph theory) , mathematics , polynomial matrix , matrix (chemical analysis) , sylvester matrix , combinatorics , difference polynomials , algebra over a field , pure mathematics , orthogonal polynomials , matrix polynomial , polynomial , mathematical analysis , materials science , composite material
We show that the sum of the ranks of two matrix polynomials is the same as the sum of the rank of the matrix obtained by applying the greatest common divisor of the polynomials, with the rank of the matrix obtained by applying the least common multiple of the polynomials. Many applications, for older or more recent problems, of this result are obtained.