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A=[4 -3; -7 8]

A =

     4    -3
    -7     8

[P,D]=eig(A)

P =

   -0.7071    0.3939
   -0.7071   -0.9191


D =

     1     0
     0    11

c=inv(P)*[10;-5]

c =

   -7.7782
   11.4237

R=[c(1) 0 0; 0 c(2) 0], E=P*R

R =

   -7.7782         0         0
         0   11.4237         0


E =

    5.5000    4.5000         0
    5.5000  -10.5000         0

R=[c(1) 0; 0 c(2)], E=P*R

R =

   -7.7782         0
         0   11.4237


E =

    5.5000    4.5000
    5.5000  -10.5000

A=[12 -7 4;6 -1 1;-12 12 -7];
[P,D]=eig(A)

P =

    0.2024    0.7071    0.2617
   -0.1215    0.7071    0.7328
   -0.9717    0.0000    0.6281


D =

   -3.0000         0         0
         0    5.0000         0
         0         0    2.0000

c= inv(P)*[10;20;25]

c =

  -21.6109
   17.9723
    6.3683

c= inv(P)*[-10;20;25]

c =

   27.7855
  -52.7384
   82.7882

R=[c(1) 0 0; 0 c(2) 0; 0 0 c(3)], E=P*R

R =

   27.7855         0         0
         0  -52.7384         0
         0         0   82.7882


E =

    5.6250  -37.2917   21.6667
   -3.3750  -37.2917   60.6667
  -27.0000   -0.0000   52.0000

clear
A=[0 0 1 0; 0 0 0 1; 25 18 0 0; 12 40 0 0];
[P,D]=eig(A)

P =

    0.0849    0.2169    0.0849    0.2169
    0.1131   -0.1085    0.1131   -0.1085
    0.5940    0.8677   -0.5940   -0.8677
    0.7920   -0.4339   -0.7920    0.4339


D =

    7.0000         0         0         0
         0    4.0000         0         0
         0         0   -7.0000         0
         0         0         0   -4.0000

c= inv(P)*[23;16;69;0]

c =

  104.2294
   47.3549
   72.5473
  -10.4768

R=[c(1) 0 0 0; 0 c(2) 0 0; 0 0 c(3) 0; 0 0 0 c(4)], E=P*R

R =

  104.2294         0         0         0
         0   47.3549         0         0
         0         0   72.5473         0
         0         0         0  -10.4768


E =

    8.8442   10.2727    6.1558   -2.2727
   11.7922   -5.1364    8.2078    1.1364
   61.9091   41.0909  -43.0909    9.0909
   82.5455  -20.5455  -57.4545   -4.5455

diary of