The Four Fundamental Subspaces and the Fundamental Theorem of Linear Algebra

Explore the four fundamental subspaces of linear algebra and the Fundamental Theorem in this 22-minute video lecture. Delve into the row space, column space, null space, and left null space of matrices, examining their relationships and dimensions. Learn how these spaces relate to R^n and R^m, and discover their orthogonal pairings. Gain a comprehensive understanding of these crucial concepts, supported by related video links for further study on column spaces, row space basis, column space basis, and null space calculations. Perfect for students and enthusiasts looking to deepen their grasp of linear algebra fundamentals.

Intro
Row Space, Column Space, and Null Space
The Four Fundamental Spaces
Subspaces of R^?
The Dimensions of the Subspaces
Spaces as Orthogonal Complements
The Fundamental Theorem of Linear Algebra
Conclusion