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Math 2890 - Sample Chapter 6 Problems

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Chapter 6

6.1      Inner Product, Length, and Orthogonality
6.2      Orthogonal Sets
6.3      Orthogonal Projections
6.4      The Gram-Schmidt Process
         Wedderburn Rank Reduction
6.5      Least-Squares Problems
6.6      Applications to Linear Models
  1. Compute the inner products of two vectors.
  2. Find a unit vector in a given direction.
  3. Find the distance between two vectors.
  4. Determine if a set is orthogonal.
  5. Project `y` onto the subspace `W`.
  6. Find the closest point to `y` in the subspace `W`
  7. Write `y` as a sum of a vector in `W` and a vector orthgonal to `W`.
  8. Find the least squares solution of the system `Ax=b.`
  9. Find the least squares error in the least squares solution of `Ax=b.`
  10. Use the QR factorization of a matrix.
  11. Find the QR factorization of a matrix.
  12. Use the QDR factorization of a matrix.
  13. Find the QDR factorization of a matrix.
  14. Find the equation of the best least-squares approximation given some data points
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