octave:2> diag([1,2,3,4]) ans = 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 octave:3> diag([1,2,3,4]') ans = 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 octave:4> (1+i)' ans = 1 - 1i octave:5> [(1+i),2].' ans = 1 + 1i 2 + 0i octave:6> diag([1,2,3,4])+diag([5,6,7],1)+diag([8,9,10],-1) ans = 1 5 0 0 8 2 6 0 0 9 3 7 0 0 10 4 octave:7> toeplitz([0,1/5,0,0],[0,4/5,0,0]) ans = 0.00000 0.80000 0.00000 0.00000 0.20000 0.00000 0.80000 0.00000 0.00000 0.20000 0.00000 0.80000 0.00000 0.00000 0.20000 0.00000 octave:8> A=rand(4) A = 0.520638 0.486704 0.785162 0.674748 0.423672 0.096238 0.990358 0.416252 0.215903 0.398611 0.949952 0.044432 0.281116 0.211076 0.269359 0.759340 octave:9> b=A*ones(4,1) b = 2.4673 1.9265 1.6089 1.5209 octave:10> x=A\b x = 1.00000 1.00000 1.00000 1.00000 octave:11> y=b'/A y = 11.23389 -0.64222 -4.83946 -7.34427 octave:12> P=toeplitz([-2,1,0,0]) P = -2 1 0 0 1 -2 1 0 0 1 -2 1 0 0 1 -2 octave:13> [V,D]=eig(P') V = 0.37175 -0.60150 -0.60150 -0.37175 -0.60150 0.37175 -0.37175 -0.60150 0.60150 0.37175 0.37175 -0.60150 -0.37175 -0.60150 0.60150 -0.37175 D = -3.61803 0.00000 0.00000 0.00000 0.00000 -2.61803 0.00000 0.00000 0.00000 0.00000 -1.38197 0.00000 0.00000 0.00000 0.00000 -0.38197 octave:14> P'*V ans = -1.34500 1.57475 0.83125 0.14200 2.17625 -0.97325 0.51374 0.22975 -2.17625 -0.97325 -0.51374 0.22975 1.34500 1.57475 -0.83125 0.14200 octave:15> V*D ans = -1.34500 1.57475 0.83125 0.14200 2.17625 -0.97325 0.51374 0.22975 -2.17625 -0.97325 -0.51374 0.22975 1.34500 1.57475 -0.83125 0.14200 octave:16> P=[0,1;1,0] P = 0 1 1 0 octave:17> P^2 ans = 1 0 0 1 octave:18> P^3 ans = 0 1 1 0 octave:19> P^4 ans = 1 0 0 1 octave:20> eig(P') ans = -1 1 octave:21> P=diag([0.5,0,0,0.5])+diag([0.5,0.5,0.5],1)+diag([0.5,0.5,0.5],-1) P = 0.50000 0.50000 0.00000 0.00000 0.50000 0.00000 0.50000 0.00000 0.00000 0.50000 0.00000 0.50000 0.00000 0.00000 0.50000 0.50000 octave:22> isstoc(P) ans = 1 octave:23> [V,D]=eig(P') V = 0.27060 0.50000 0.65328 0.50000 -0.65328 -0.50000 0.27060 0.50000 0.65328 -0.50000 -0.27060 0.50000 -0.27060 0.50000 -0.65328 0.50000 D = -0.70711 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 0.70711 0.00000 0.00000 0.00000 0.00000 1.00000 octave:24> v=V(:,4)'/norm(V(:,4),1) v = 0.25000 0.25000 0.25000 0.25000 octave:25> v*P ans = 0.25000 0.25000 0.25000 0.25000 octave:26> invariantPotenze(P,1e-6,100) ans = 0.25000 0.25000 0.25000 0.25000 octave:27> [v,iter]=invariantPotenze(P,1e-6,100) v = 0.25000 0.25000 0.25000 0.25000 iter = 36 octave:28> diary off