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Next: Basic Course CPS615

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• Basic Course CPS615 Contact Points
• Course Structure
• Definition of a Matrix
• The Definition of a Vector
• The Definition of Scalar Products and Orthonormality
• Types of Matrices
• Eigenvectors and Eigenvalues
• Structure of Matrix
• Equations for Eigenvalues---I
• Equations for Eigenvalues---II
• Polynomial Equations for Eigenvalues
• General Properties of Eigenvalues
• Eigenvalues of Hermitean Matrices---I
• Eigenvalues of Hermitean Matrices---II
• Orthogonality of Eigenvectors of Hermitean Matrices
• Orthonormal Eigenvectors and Unitary Transformation Matrices
• Diagonal Form of General Hermitean Matrix---I
• Diagonal Form of General Hermitean Matrix---II
• Eigenvectors and Eigenvalues of Symmetric Matrices
• Finite and Infinite Dimensional Matrices as Operators
• as an Operator and Its Scalar Products
• as a Hermitean Operator
• The Laplacian as a (Matrix) Operator
• Mapping of Function Spaces to a Finite Number of Dimensions

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Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu