ST790R -- Fall 2009

  Homework #1 -- due Thursday, 03 September 2009

  Exercises in Textbook:
   2.14, 2.15 (on the computer you are using...)

  R Exercises:

  1) Let u = ( 1, 2, 3, 3, 2, 1)'.  Compute U = I - (2/d) u u' where
    d = u'u.  (This type of matrix is known as an 'elementary
    reflector' or a 'Householder transformation.')
  2) Find the largest and smallest off-diagonal elements of U*U.
  3) Find the largest and smallest diagonal elements of U*U.
  4) Compute U*u.
  5) Compute max_i sum_j abs(U(i,j))
  6) Print the second row of U.
  7) Print the elements of the second column below the diagonal. 
  8) Let A be the first three columns of U.  Compute P = AA'.
  9) Show that P is idempotent by recomputing (5) with P*P-P.
  10) Let B be the last three columns of U.  Compute Q = BB'.
  11) Show that Q is idempotent by recomputing (5) with Q*Q-Q.
  12) Compute P+Q.