Special matrices have special eigenvalues and eigenvectors. Symmetric and positive definite matrices have extremely nice properties, and studying these matrices brings together everything we’ve learned about pivots, determinants and eigenvalues. In this session we also practice doing linear algebra with complex numbers and learn how the pivots give information about the eigenvalues of a symmetric matrix.
Lecture Video and Summary
- Watch the video lecture Lecture 25: Symmetric Matrices and Positive Definiteness
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 6.4 through 6.5 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Problem Solving: Symmetric Matrices and Positive Definiteness
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you’re done.