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Math 2890 - Sample Chapter 7 Problems

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Chapter 7

7.1      Diagonalization of Symmetric Matrices
         Schur Decomposition
7.2      Quadratic Forms
7.3      Constrained Optimization
7.4      The Singular Value Decomposition
7.5      Applications to Image Processing and Statistics
         The Great Human Diasporas
         Text Retrieval Algorithms
  1. Create a matrix with prescribed properties.
  2. Orthogonally diagonalize a matrix.
  3. Find the matrix of a quadratic form.
  4. Compute the quadratic form `Q(x)=x^T Ax` given `A.`
  5. Maximize `x^TAx` subject to `x^Tx=1.`
  6. Find vector at which `x^TAx` is maximized subject to `x^Tx=1`
  7. Use the singular value decomposition of a matrix.
  8. Find the singular value decomposition of a matrix.
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