On Nonsingularity of RSFPLR Circulant Matrices
Xiyou Cui
Library, Shandong Normal University, Jinan, Shandong, 250014, China.
Nan Jiang *
Linyi University, Linyi 276000, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we discuss the non-singularity of a row skew rst-plus-last right (RSFPLR) circulant matrices with the rst row (a1; a2; : : : ; an),which is determined by entries of the first row. First,the suffient condition for the matrix to be nonsingular is that,there exists an element ai0 belonging to the first row,whose absolute value is greater than the sum of the corresponding power of 2 and the absolute values of the remaining (n − 1) elements, that is, $$|a_{i_0}|>\sum_{{i=1},{i\neq i_0}}^{n}2^{i-i_0}|a_i|.$$ Moreover, we derive other suffcient conditions for judging the non-singularity of the matrix.
Keywords: RSFPLR circulant matrix, non-singularity, singularity.