Advanced Linear Algebra - Lecture 38: Introduction to the Pseudoinverse

We introduce the (Moore-Penrose) pseudoinverse of a matrix, which exists for all matrices (and equals the usual inverse if it exists). We show how to compute the pseudoinverse via the singular value decomposition. Textbook: http://www.njohnston.ca/publications/advanced-linear-and-matrix-algebra/ Blank course notes (lectures 38-41): http://www.njohnston.ca/ala_week10.pdf Annotated course notes (lectures 38-41): http://www.njohnston.ca/ala_week10_annotated.pdf Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction 00:47 - Invertibility and linear systems 03:52 - Pseudoinverse definition 08:25 - 3x4 example