Title of article :
GENERALIZATION OF SOME DETERMINANTAL IDENTITIES FOR NON-SQUARE MATRICES BASED ON RADIC’S DEFINITION
Author/Authors :
AMIRI, A. iran university of science and technology - Computer Engineering Department, تهران, ايران , AMIRI, A. zanjan university - Computer Engineering Department, زنجان, ايران , FATHY, M. iran university of science and technology - Computer Engineering Department, تهران, ايران , FATHY, M. zanjan university - Computer Engineering Department, زنجان, ايران , BAYAT, M. zanjan university - Computer Engineering Department, زنجان, ايران
Abstract :
In this paper, we focus on Radic’s definition for the determinant of non-square matrices. We develop some important properties of this determinant. We generalize several classical important determinant identities, including Dodgson’s condensation, Cauchy-Binet, and Trahan for non-square matrices. Also, we propose an efficient algorithm with θ((mn)^2) time complexity for computing Radic’s determinant based on Dodgson algorithms and dynamic programming technique.
Keywords :
Radic’s determinant , non , square matrix , determinantal identities , Binet , Cauchy formula , Dodgson’s algorithm , Trahan formula , dynamic programing
Journal title :
TWMS Journal of Pure and Applied Mathematics
Journal title :
TWMS Journal of Pure and Applied Mathematics
