18.06SC | Fall 2011 | Undergraduate

Linear Algebra

Unit III: Positive Definite Matrices and Applications

Symmetric Matrices and Positive Definiteness

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

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.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 6.4 through 6.5 in the 4th or 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

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Course Info

Departments
As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Simulations
Course Introduction
Instructor Insights