  There have been several algorithms designed to optimise matrix
multiplication. From schoolbook method with complexity $O(n^3)$ to advanced
tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible
bound achieved), a lot of work has been done to reduce the steps used in the
recursive version. Some group-theoretic and computer algebraic estimations also
conjecture the existence of an $O(n^2)$ algorithm. This article discusses a
quadratic-time number-theoretic approach that converts large vectors in the
operands to a single large entity and combines them to make the dot-product.
For two $n \times n$ matrices, this dot-product is iteratively used for each
such vector. Preprocessing and computation makes it a quadratic time algorithm
with a considerable constant of proportionality. Special strategies for
integers, floating point numbers and complex numbers are also discussed, with a
theoretical estimation of time and space complexity.
