On Tue Nov 2 11:31:09 EDT 2010

## This example is from P.247 of "Linear Algebra", by Friedberg, Insel and Spence.


> G := <<1,4>|<3,2>>; Goft := G - t*eye(2);

            [1    3]            [1 - t      3  ]
       G  = [      ] ,  Goft  = [              ]
            [4    2]            [  4      2 - t]


>  fGt := Det(Goft) = factor(fGt) ;

                        2
   fGt  =  -10 - 3 t + t    =   (t + 2) (t - 5)

 

> GN2 := G - (-2)*eye(2);  G5 := G - (5)*eye(2);
 
             [3    3]             [-4     3]
      GN2  = [      ] ,    G5  =  [        ]
             [4    4]             [ 4    -3]

> rrefGN2  := RREF(GN2) ; rrefG5  := RREF(G5) ; 

             [1    1]             [1    -3/4]
  rrefGN2  = [      ] ,  rrefG5 = [         ]
             [0    0]             [0     0  ]

> v1 := <-1,1>;   v2 := <3,4>; G . v1; G . v2;

            [-1]            [3]
      v1  = [  ] ,    v2  = [ ]
            [ 1]            [4]

            [ 2]            [15]
            [  ] , 	    [  ]
            [-2]	    [20]

>  C := <v1 | v2>;  Dmat  := MI(C) . G . C; 

       [-1    3]               [-2    0]
  C  = [       ] ,     Dmat  = [       ]
       [ 1    4]               [ 0    5]

> IsThisG := C . Dmat . MI(C);  G := G ;

	       [1    3]           [1    3]
    IsThisG  = [      ] ,    G  = [      ]
	       [4    2]	          [4    2]

## So we have succeeded in conjugating G to a diagonal matrix.