Lesson 19 of 20 · about 18 min

Symmetric matrices and the SVD

Every matrix, of any shape, does the same three things. It turns, it stretches along perpendicular directions, and it turns again. That's the singular value decomposition, often called the most useful fact in linear algebra. You'll watch a circle become an ellipse in three moves, meet the symmetric matrices whose eigenvectors are always perpendicular, and find the best one-pattern summary of a table of data.