Symmetric matrices and Positive Definite matrices

Symmetric matrices and Positive Definite matrices
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Taught by OCW
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
Symmetric matrices and Positive Definite matrices -- Lecture 25. Special properties of these matrices and why they are important.
  • 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?
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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Reviewed by MathVids Staff on November 23, 2008.
 
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