Paravartya Yojayet : The Future of High – Speed Linear Computation

Abstract

This dissertation explores the application of Vedic Mathematics, specifically the Paravartya Yojayet sutra[3], as an efficient alternative to traditional algebraic methods for solving systems of linear equations. While conventional techniques like Gaussian elimination, substitution, and Cramer’s Rule are robust, they often involve complex procedural steps that increase the risk of manual error and computational load as the number of variables grows. Through a comparative analysis and detailed mathematical demonstrations, this research shows that the Vedic approach facilitates a direct "dimensional reduction,[5]" allowing systems of four variables to be collapsed into two-variable subsets in a single logical transition. The study highlights the method's superiority in terms of speed, reduced cognitive load, and its potential for modern technological integration in fields such as Aerospace trajectory calculation, Robotic inverse kinematics, and digital circuitry design. Ultimately, the research advocates for the integration of these ancient mathematical principles into contemporary STEM curricula to enhance pedagogical effectiveness and computational efficiency.