Generalization of Dodgson’s condensation method for calculating determinant of rectangular matrices

In this paper, we present generalization of Dodgson’s condensation method for calculating determinant of rectangular matrices. Based on the Dodgson’s generalization method to reduce the order of rectangular determinant to second order square determinant, we have further identified nine different cases that can be used to determine pivot block, which can be useful to determine the block with highest number of elements equal to zero, since the block with highest zeros is calculated faster than other blocks, hence there is an effect on the overall execution time of the determinant calculation. We have also presented the specific computer algorithms for each theorem/case, and tested in MATLAB environment, where we noted that the newly presented algorithm is executed faster than the existing one.