Many calculations become simpler when performed using orthonormal vectors or othogonal matrices. In this session, we learn a procedure for converting any basis to an orthonormal one.
Lecture Video and Summary
- Watch the video lecture Lecture 17: Orthogonal Matrices and Gram-Schmidt
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 4.4 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Problem Solving: Gram-Schmidt Orthogonalization
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you’re done.