Generalization of Some Determinantal Identities for Non-square Matrices Based on Radic’s Definition

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)) time complexity for computing Radic’s determinant based on Dodgson algorithms and dynamic programming technique.