Advanced Linear Algebra - Lecture 36: The Fundamental Matrix Subspaces from the SVD

We talk about how to construct orthonormal bases of the four fundamental matrix subspaces (the range, null space, and range and null space of the adjoint) via the singular value decomposition. As a corollary, we learn that range(A) is orthogonal to null(A^*), and range(A^*) is orthogonal to null(A). Textbook: http://www.njohnston.ca/publications/... Blank course notes (lectures 34-37): http://www.njohnston.ca/ala_week9.pdf Annotated course notes (lectures 34-37): http://www.njohnston.ca/ala_week9_ann... Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction 04:17 - Main theorem 11:31 - Orthogonality corollary 13:37 - 3x4 example