Positive definite matrices (tests), Tests for minimum, and Ellipsoids in R^n

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Taught by OCW
  • Currently 4.0/5 Stars.
6655 views | 1 rating
Lesson Summary:

In this lecture, the focus is on positive definite matrices and how to determine if a matrix is positive definite. Different tests, such as eigenvalues, determinants, and pivots, are explored for 2 by 2 matrices. Additionally, the concept of X transpose AX is introduced and used as a guide for recognizing positive definite matrices. The lecture also touches on the significance of positive definiteness and how it is connected to the geometry of ellipsoids. Overall, the lecture provides a comprehensive understanding of positive definite matrices and their importance in linear algebra.

Lesson Description:

Positive definite matrices (tests), Tests for minimum, and Ellipsoids in R^n -- Lecture 27. Learn how to determine if a matrix is positive definite and how to test a matrix for a minimum.

Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms

Additional Resources:
Questions answered by this video:
  • How do you test to see if a matrix is positive definite?
  • How do you test a matrix for minimum?
  • What are ellipsoids in R^n?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video incorporates a lot of Calculus 2 and 3 to test for minimum points and discusses how this relates to positive definite matrices. A good geometrical explanation and view of matrices and Linear Algebra. Ellipsoids in R^n are also discussed.