Explore the fascinating world of coupled oscillators and matrix theory in this comprehensive lecture from the Summer School for Women in Physics 2024. Delve into the mathematical foundations and physical applications of coupled systems as Dr. Supurna Sinha guides you through key concepts. Learn how matrices can be used to analyze and describe the behavior of interconnected oscillators, gaining valuable insights into this important area of physics. Discover the interconnectedness of mathematical tools and physical phenomena while developing problem-solving skills applicable to a wide range of scientific disciplines.