Analysis of faster matrix multiplication

Abstract

Since the definition of matrices in 1855, matrix multiplication has played a crucial role in a wide range of fields. Over the years, numerous researchers have dedicated their efforts to improving the time complexity of this fundamental operation. This paper aims to delve into the historical development of matrix multiplication algorithms and methodologies employed to achieve these significant advancements in time complexity. By employing various approaches, researchers have been able to improve the time complexity of matrix multiplication, leading to a significant reduction from O () to O (). Across nearly two centuries, this progress is contributed by a lot of extraordinary scientists and researchers. This paper explores the practical implications of these improvements across various domains, such as computer science, physics, economics, and more. The development of more efficient matrix multiplication algorithms has enabled researchers and practitioners to tackle complex problems and explore new frontiers. In the future, with the rapid growth of machine learning techniques, matrix multiplication will continue to evolve and improve.