%%%% Sta of "RREF-Complexes.Lisp.txt"

;; Uses a semicolon ";" to start a comment.
;; Use "::::" to indicate a new problem or section.
;; Use "%" for the Lisp prompt.

  :::: Reducing a Complex-matrix ::::

% (use-ring GaussRational-ring)


% (setq G (mat-make-initseq 3 3 (list 
         1      #C(-2 -2)       #C(1 -1)  
 #C(-1 -2)      #C(1 -1)        #C(-1 -1)  
 #C(0 -1)       #C(-2 -2)       #C(-1 1)  
    )))

    [      1  -2-2i   1-i ]
    [  -1-2i    1-i  -1-i ]
    [     -i  -2-2i  -1+i ]


% (rref-mtab-beforecol G :stepwise t)


  Reducing column-0 produces

       c0   c1   c2      Row operations
   |------------------|
r0 |    1  -2-2i  1-i |  1     0    0
r1 |    0   3-7i  2   |  1+2i  1    0
r2 |    0    -4i   2i |     i  0    1
   |------------------|


  Reducing column-1 produces

       c0   c1         c2                    Row operations
   |------------------------------|
r0 |    1    0  (21/29)-(9/29)i   |     (5/29)+(2/29)i  (-4/29)+(10/29)i    0
r1 |    0    1  (3/29)+(7/29)i    |  (-11/58)+(13/58)i    (3/58)+(7/58)i    0
r2 |    0    0  (-28/29)+(70/29)i |   (-26/29)+(7/29)i  (-14/29)+(6/29)i    1
   |------------------------------|


  Reducing column-2 produces

       c0   c1   c2                          Row operations
   |------------------|
r0 |    1    0    0   |  (-1/14)-(1/14)i   (-2/7)+(2/7)i   (3/14)+(3/14)i
r1 |    0    1    0   |    (-1/7)+(1/7)i  (1/14)+(1/14)i  (-1/14)+(1/14)i
r2 |    0    0    1   |    (3/14)+(2/7)i    (1/7)+(1/7)i   (-1/7)-(5/14)i
   |------------------|

  JK: Found 3 pivots before the third column.



% (setq InvG (MTB-ROM *Tab*))

    [  (-1/14)-(1/14)i   (-2/7)+(2/7)i   (3/14)+(3/14)i ]
    [    (-1/7)+(1/7)i  (1/14)+(1/14)i  (-1/14)+(1/14)i ]
    [    (3/14)+(2/7)i    (1/7)+(1/7)i   (-1/7)-(5/14)i ]

% (mat-mul  InvG G)   ;;Checking, by multiplying.

    [  1  0  0 ]
    [  0  1  0 ]
    [  0  0  1 ]


%%%% End of "RREF-Complexes.Lisp.txt"