octave:2> A=rand(4) A = 0.916605 0.306759 0.254480 0.108627 0.974223 0.174484 0.468015 0.098693 0.247707 0.274469 0.634634 0.045661 0.373121 0.647467 0.591584 0.344521 octave:3> b=rand(4,1) b = 0.87647 0.56334 0.36526 0.31464 octave:4> y=b'/A y = 0.61701 0.15780 -0.47474 0.73646 octave:5> y*A ans = 0.87647 0.56334 0.36526 0.31464 octave:6> b' ans = 0.87647 0.56334 0.36526 0.31464 octave:7> A/b error: operator /: nonconformant arguments (op1 is 4x4, op2 is 4x1) octave:7> A/b' ans = 0.83714 0.87572 0.46883 0.77108 octave:8> A A = 0.916605 0.306759 0.254480 0.108627 0.974223 0.174484 0.468015 0.098693 0.247707 0.274469 0.634634 0.045661 0.373121 0.647467 0.591584 0.344521 octave:9> sum(A,2) ans = 1.5865 1.7154 1.2025 1.9567 octave:10> P=spdiags(sum(A,2),0,4,4)\A P = 0.577763 0.193359 0.160406 0.068471 0.567922 0.101715 0.272829 0.057533 0.205998 0.228254 0.527775 0.037973 0.190690 0.330899 0.302339 0.176073 octave:11> sum(P,2) ans = 1.00000 1.00000 1.00000 1.00000 octave:12> [V,D]=eig(P') V = -0.768212 -0.671503 0.436368 0.598690 -0.341301 0.029063 -0.322181 -0.777571 -0.529903 0.734665 0.534203 0.191798 -0.112095 -0.092225 -0.648390 -0.012917 D = Diagonal Matrix 1.000000 0 0 0 0 0.353999 0 0 0 0 0.127295 0 0 0 0 -0.097967 octave:13> v=V(:,1) v = -0.76821 -0.34130 -0.52990 -0.11210 octave:14> norm(v) ans = 1 octave:15> v=v/sum(v) v = 0.438599 0.194861 0.302540 0.063999 octave:16> sum(v) ans = 1 octave:17> v v = 0.438599 0.194861 0.302540 0.063999 octave:18> v*P error: operator *: nonconformant arguments (op1 is 4x1, op2 is 4x4) octave:18> v=v' v = 0.438599 0.194861 0.302540 0.063999 octave:19> v*P ans = 0.438599 0.194861 0.302540 0.063999 octave:20> P P = 0.577763 0.193359 0.160406 0.068471 0.567922 0.101715 0.272829 0.057533 0.205998 0.228254 0.527775 0.037973 0.190690 0.330899 0.302339 0.176073 octave:21> invariantPotenze(P,1e-6,100) ans = 0.438599 0.194861 0.302541 0.063999 octave:22> [v,iter]=invariantPotenze(P,1e-6,100) v = 0.438599 0.194861 0.302541 0.063999 iter = 13 octave:23> [v,iter]=invariantPotenze([0,1;1,0],1e-6,100) warning: Impossibile raggiungere la tolleranza richiesta warning: entro il numero massimo di iterazioni consentito. v = 0.33284 0.66716 iter = 100 octave:24> eig([0,1:1,0]) error: eig: argument must be a square matrix octave:24> eig([0,1;1,0]) ans = -1 1 octave:25> [v,iter]=invariantPotenze([0,1;1,0],1e-6,100) warning: Impossibile raggiungere la tolleranza richiesta warning: entro il numero massimo di iterazioni consentito. v = 0.12068 0.87932 iter = 100 octave:26> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.20104 0.79896 iter = 1 octave:27> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.74312 0.25688 iter = 1 octave:28> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.53426 0.46574 iter = 1 octave:29> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.46786 0.53214 iter = 1 octave:30> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.64320 0.35680 iter = 1 octave:31> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.51403 0.48597 iter = 1 octave:32> [v,iter]=invariantPotenze([1,0;0,1],1e-6,100) v = 0.968370 0.031630 iter = 1 octave:33> [v,iter]=invariantPotenze([0,1;1,0],1e-6,100) warning: Impossibile raggiungere la tolleranza richiesta warning: entro il numero massimo di iterazioni consentito. v = 0.33115 0.66885 iter = 100 octave:34> v*[0,1;1,0] ans = 0.66885 0.33115 octave:35> [V,D]=eig([0,1;1,0]) V = -0.70711 0.70711 0.70711 0.70711 D = Diagonal Matrix -1 0 0 1 octave:36> [0,0,0,0]/(P-eye(4)) warning: matrix singular to machine precision, rcond = 1.97747e-17 ans = 0 0 0 0 octave:37> (P-eye(4))'\[0;0;0;0] warning: matrix singular to machine precision, rcond = 1.97747e-17 ans = 0 0 0 0 octave:38> [0,0,0,0,1]/([P-eye(4),ones(4,1)]) ans = 0.438599 0.194861 0.302540 0.063999 octave:39> diary off