In this lesson, we dive into the concept of similar matrices and their connection to eigenvalues. Similar matrices are two square matrices that are connected by some invertible matrix. They may not look the same, but they have something important in common: the same eigenvalues. We explore this idea with examples and show how it can be applied in different contexts. Additionally, we touch upon positive definite matrices and how they come about in physical problems. Overall, this lesson provides a deeper understanding of these key concepts in linear algebra.
Similar Matrices and Jordan Form -- Lecture 28. Learn what similar matrices are and a bit more about positive definite matrices. Also, Jordan Form is explained.
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
Questions answered by this video:
What are positive definite matrices?
What is Jordan Form?
What are similar matrices?
What does it mean for matrices to be similar?
Where do positive definite matrices come from?
Currently 4.0/5 Stars.
This video does some more to explain tests for positive definite matrices, and introduces similar matrices. A good introduction to these very interesting matrices. Jordan Form is also explained well in this video.