7 videos in "Matrices and Matrix Operations"
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Elimination with Matrices
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Multiplication and Inverse Matrices
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Matrix Spaces, Rank 1 matrices, and Small World Graphs
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Graphs, Networks, and Incidence Matrices
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Symmetric matrices and Positive Definite matrices
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Positive definite matrices (tests), Tests for minimum, and Ellipsoids in R^n
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Similar Matrices and Jordan Form
Symmetric matrices and Positive Definite matrices
Symmetric matrices and Positive Definite matrices
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Part of video series Linear Algebra Course acquired through MIT OpenCourseWare
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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
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.
- 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.
- 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.
