Symmetric matrices and Positive Definite matrices

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Lesson Description:

Symmetric matrices and Positive Definite matrices -- Lecture 25. Special properties of these matrices and why they are important.

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:

Symmetry Mini-Lecture - This is a mini-lecture demo lesson on Symmetry and symmetric matrices.
Positive Definite Mini-Lecture - This is a mini-lecture demo lesson on Positive Definite matrices.

Questions answered by this video:

What is a symmetric matrix?
What is special about Eigenvalues of a symmetric matrix?
What is special about Eigenvectors of a symmetric matrix?
What is a positive definite matrix?
When are Eigenvalues real?

Staff Review
- Currently 4.0/5 Stars.
This lesson introduces symmetric matrices where A = A transpose. Eigenvalues and Eigenvectors have some special properties in these cases. Also, positive definite matrices are discussed. A good explanation of a very interesting class of matrices.

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