Tensors and Their Uses, Especially for Matrix Multiplication - Part 1

Learn about tensors and their applications across multiple fields in this comprehensive lecture from the Complexity and Linear Algebra Boot Camp at Simons Institute. Begin with a gentle introduction to tensors and discover how they emerge in combinatorics, signal processing, geometry, and complexity theory. Focus on the geometric aspects of tensors that are most relevant for understanding the complexity of matrix multiplication. Explore fundamental tensor concepts and their mathematical foundations while building toward more advanced applications in computational complexity. Gain insights into how tensor methods provide powerful tools for analyzing algorithmic efficiency and mathematical structures across diverse domains.