GNU Octave, version 2.1.36 (i686-pc-linux-gnu).
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 John W. Eaton.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTIBILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, type `warranty'.

Report bugs to <bug-octave@bevo.che.wisc.edu>.

octave> california
ans =

  0  0  0

p =

   30
    4
  100

p1 =

   29.6580
    4.2140
  100.1280

p100 =

   13.280
   14.574
  106.147

p1000 =

    9.4487
   17.1794
  107.3719

octave> A
A =

  0.9850000  0.0020000  0.0010000
  0.0050000  0.9910000  0.0010000
  0.0100000  0.0070000  0.9980000

octave> eig(A)
ans =

  1.00000
  0.98339
  0.99061

octave> [S, L]=eig(A)
S =

  -0.086569  -0.810499  -0.098784
  -0.157397   0.490799  -0.652521
  -0.983734   0.319700   0.751304

L =

  1.00000  0.00000  0.00000
  0.00000  0.98339  0.00000
  0.00000  0.00000  0.99061

octave> c=S(:,1)
ans =

  -0.086569
  -0.157397
  -0.983734

octave> c=S(:,1)
c =

  -0.086569
  -0.157397
  -0.983734

octave> [1,1,1]*c
ans = -1.2277
octave> c = c / ([1,1,1]*c)
ans =

  0.070513
  0.128205
  0.801282

octave> c = c / ([1,1,1]*c)
c =

  0.070513
  0.128205
  0.801282

octave> A*c
ans =

  0.070513
  0.128205
  0.801282

octave> A^10000
ans =

  0.070513  0.070513  0.070513
  0.128205  0.128205  0.128205
  0.801282  0.801282  0.801282

octave>