Introduction to Non-Commutative Optimization - Matrix and Operator Scaling

Explore the fundamentals of non-commutative optimization through this lecture delivered at the Simons Institute's Complexity and Linear Algebra Boot Camp. Learn about optimization problems that arise from group actions on vector spaces and discover their wide-ranging applications across computer science, quantum information, machine learning, and mathematics. Focus on two well-established problems - matrix scaling and operator scaling - as entry points into this specialized field. Gain insights into how these mathematical frameworks connect abstract algebraic concepts with practical optimization challenges. Understand the theoretical foundations that make non-commutative optimization a powerful tool for solving complex problems in multiple disciplines.