GENERALIZATION OF SOME DETERMINANTAL IDENTITIES FORNON-SQUARE MATRICES BASED ON RADIC’S DEFINITIONA. AMIRI, M. FATHY, M. BAYAT (pp. 163-175)
In this paper, we focus on Radic’s definition for the determinant of non-squarematrices. We develop some important properties of this determinant. We generalize severalclassical 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 dynamicprogramming technique.
Radic’s determinant, non-square matrix, determinantal identities, Binet-Cauchyformula, Dodgson’s algorithm, Trahan formula, dynamic programing.