We learn how to change coordinate vector from one basis to another by constructing change-of-basis matrices. Textbook: http://www.njohnston.ca/publications/advanced-linear-and-matrix-algebra/ Blank course notes (lectures 5-8): http://www.njohnston.ca/ala_week2.pdf Annotated course notes (lectures 5-8): http://www.njohnston.ca/ala_week2_annotated.pdf Please leave a comment below if you have any questions, comments, or corrections.