Nikhil Sharma L&S Sciences
Analysis of Matrix Multiplication Complexity Using Properties of Tensors
Matrix multiplication is one of the most fundamental operations in mathematics, and its usage is extensively pervasive in modern-day computer systems; innumerable algorithms employ techniques from linear algebra in their implementation. As a result, it’s critical to perform matrix multiplication as quickly as possible to ensure the smooth and efficient performance of everyday computer applications. It’s been shown in existing literature that there is an intrinsic relationship between properties of matrix multiplication and a special geometric object known as a tensor. To date, an extensive exploration observing this relationship in specific cases has not been performed. In my research project, I plan to conduct a detailed mapping of how these properties of tensors correspond to matrix multiplication and their effect on the time complexity of performing the multiplication. As a dual major in computer science, this problem is especially interesting and relevant to me, and I look forward to contributing towards a breakthrough in the field.