Homework on Matrix Algebra
(Check on Matlab)

X =
 

7

1

4

3

3

3

1

7

4

5

5

5

4

4

4

J =
 

1

1

1

1

1


 

C =
 

.5

0

.5

0

0

1


Compute and Interpret

  1. m = (J'X)/5
  2. M = (Jm)
  3. S = (X-M)'(X-M)/4
  4. D = diag[sqrt(s11), sqrt(s22),sqrt(s33)]
  5. R = D-1SD-1
  6. Y = XC
  7. A = JJ'Y/5
  8. V = (Y-A)'(Y-A)/4
  9. W = C'SC
  10. F = [X1 | X2 ],  where X1 and X2 are the first two columns of X
  11. G = X3   where X3 is the last column of X
  12. B = (F'F)-1F'G
  13. Z = FB
  14. E = (Y2 - Z)

Compute the eigenvalues of S and V

Show the following are true (using definitions above):

  1. (X-M)C = XC - MC
  2. (XC)' = C'X'

Show that FB does not equal BF, and the latter does not even exist
(using definitions above).