Special Homework Problem due Thursday, Oct 21:

Let M be the 5x5 real matrix, J - 2I =

-1 +1 +1 +1 +1
+1 -1 +1 +1 +1
+1 +1 -1 +1 +1
+1 +1 +1 -1 +1
+1 +1 +1 +1 -1

Factor this matrix into an orthogonal matrix, Q,
and an upper triangular matrix, R.

/* This matrix is related to Textbook Problem 4.4.17 */


In order to ease the grader's work, try to conform to the following
notational conventions:

Let the five columns of M be  M = a|b|c|d|e

Let the five columns of Q be q1, q2, q3, q4, and q5.

Let any preliminary (unnormallized) scalar multiples of these
column vectors be denoted by q1', q2', etc


Avoid drifting far off course by CHECKING YOUR WORK at
each stage:

  Is your q1^T q1 = 1 ?
  Does your q2' satisfy q1^T q2' = 0?
  Is your q2^T q2 = 1 ?
  Does your q3' satisfy q1^T q3' = 0?
  Does your q3' satisfy q2^T q3' = 0?
  Is your q3^T q3 = 1 ?
   ...


Results will be posted on the net.


EXTRA credit:

When you have found the final Q and R matrices, do you see any
reasonably simple formula for their coefficients?



/* SOLUTION to this problem can be found in latter sections of the file
 Oct21.QR, which is in this same directory
*/