Advanced Linear Algebra - Lecture 39: Using the Pseudoinverse to Solve Linear Systems

We show that the pseudoinverse of a matrix provides the best solution of a linear system, regardless of whether the linear system has a unique solution, infinitely many solutions, or no solutions. In the process, we develop the linear least squares method for constructing the line of best fit for a set of data points. Textbook: http://www.njohnston.ca/publications/... 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_an... Please leave a comment below if you have any questions, comments, or corrections. CORRECTIONS: At 4:35, the index variable in all summations should be j (not r, as in one of the summations). That is, the 2nd summation on the line that appears at this time stamp should be a sum from j = 1 to r, not from r = 1 to r. Timestamps: 00:00 - Introduction 00:51 - Unique or infinitely many solutions 07:12 - 3x3 example 09:34 - No solutions (linear least squares) 11:30 - Line of best fit example 18:50 - Summary