Matrix Transpose Isn't Just Swapping Rows and Columns

Explore a comprehensive 26-minute video lecture that delves into the concept of matrix transpose, challenging the common misconception that it's simply about swapping rows and columns. Learn how to visualize transpose through the lens of linear map theory and covectors, gaining insights into its applications in special relativity, general relativity, and quantum mechanics. Discover a unique approach to understanding transpose that differs from traditional singular value decomposition methods. Engage with in-depth explanations of covectors as measuring devices, the relationship between transpose and adjoints, and the subtleties of vector-covector correspondence in relativity. Benefit from detailed chapter breakdowns, further reading suggestions, and opportunities for viewer engagement through Q&A forms and social media platforms.

Introduction
Chapter 1: The big picture
Chapter 2: Visualizing covectors
Chapter 3: Visualizing transpose
Two other examples of transpose
Chapter 4: Subtleties special relativity?