diag([1,2,3,4]) ans = 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 diag([1,2,3,4]') ans = 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 diag([1,2,3,4])+diag([5,6,7],1) ans = 1 5 0 0 0 2 6 0 0 0 3 7 0 0 0 4 toeplitz([0,1,0,0],[0,2,0,0]) ans = 0 2 0 0 1 0 2 0 0 1 0 2 0 0 1 0 toeplitz([0,1,0,0]) ans = 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 v=[1,2,3,4] v = 1 2 3 4 v' ans = 1 2 3 4 v.' ans = 1 2 3 4 v=[1+i,2-i] v = 1.0000 + 1.0000i 2.0000 - 1.0000i v' ans = 1.0000 - 1.0000i 2.0000 + 1.0000i v.' ans = 1.0000 + 1.0000i 2.0000 - 1.0000i for i=1:3 disp('ciao') end ciao ciao ciao 1+i ans = 4 1i ans = 0 + 1.0000i 2i ans = 0 + 2.0000i 2*i ans = 6 A=rand(4) A = 0.8147 0.6324 0.9575 0.9572 0.9058 0.0975 0.9649 0.4854 0.1270 0.2785 0.1576 0.8003 0.9134 0.5469 0.9706 0.1419 b=rand(4,1) b = 0.4218 0.9157 0.7922 0.9595 b=A*ones(4,1) b = 3.3618 2.4536 1.3634 2.5727 A\b ans = 1.0000 1.0000 1.0000 1.0000 y=b'/A y = -33.0320 4.5548 35.7659 23.6554 y*A ans = 3.3618 2.4536 1.3634 2.5727 b' ans = 3.3618 2.4536 1.3634 2.5727 (A'\b)' ans = -33.0320 4.5548 35.7659 23.6554 y y = -33.0320 4.5548 35.7659 23.6554 P=rand(5) P = 0.6557 0.7577 0.7060 0.8235 0.4387 0.0357 0.7431 0.0318 0.6948 0.3816 0.8491 0.3922 0.2769 0.3171 0.7655 0.9340 0.6555 0.0462 0.9502 0.7952 0.6787 0.1712 0.0971 0.0344 0.1869 sum(P,2) ans = 3.3817 1.8871 2.6009 3.3811 1.1684 d=sum(P,2) d = 3.3817 1.8871 2.6009 3.3811 1.1684 D=diag(1./d) D = 0.2957 0 0 0 0 0 0.5299 0 0 0 0 0 0.3845 0 0 0 0 0 0.2958 0 0 0 0 0 0.8559 Q=D*P Q = 0.1939 0.2241 0.2088 0.2435 0.1297 0.0189 0.3938 0.0169 0.3682 0.2022 0.3265 0.1508 0.1065 0.1219 0.2943 0.2762 0.1939 0.0137 0.2810 0.2352 0.5809 0.1465 0.0831 0.0295 0.1599 sum(Q,2) ans = 1.0000 1.0000 1.0000 1.0000 1.0000 d=sum(P,2); D=diag(1./d); Q=D*P; 3*(1/3) ans = 1 3*(1/3)==1 ans = 1 49*(1/49)==1 ans = 0 49/49==1 ans = 1 D=diag(d) D = 3.3817 0 0 0 0 0 1.8871 0 0 0 0 0 2.6009 0 0 0 0 0 3.3811 0 0 0 0 0 1.1684 Q=D\P; sum(Q,2) ans = 1.0000 1.0000 1.0000 1.0000 1.0000 D=diag(d) D = 3.3817 0 0 0 0 0 1.8871 0 0 0 0 0 2.6009 0 0 0 0 0 3.3811 0 0 0 0 0 1.1684 spdiags(d,0,5,5) ans = (1,1) 3.3817 (2,2) 1.8871 (3,3) 2.6009 (4,4) 3.3811 (5,5) 1.1684 D=spdiags(d,0,5,5); Q=D\P; sum(Q,2) ans = 1.0000 1.0000 1.0000 1.0000 1.0000 P=randstoc(3) P = 0.2607 0.3776 0.3618 0.2402 0.4068 0.3531 0.5957 0.2544 0.1499 sum(P,2) ans = 1 1 1 P=randstoc(4); [V,D]=eig(P') V = Columns 1 through 2 0.4733 -0.0741 - 0.2883i 0.4530 -0.5654 - 0.0883i 0.7080 0.6644 0.2635 -0.0248 + 0.3766i Columns 3 through 4 -0.0741 + 0.2883i -0.0058 -0.5654 + 0.0883i -0.7661 0.6644 0.6259 -0.0248 - 0.3766i 0.1461 D = Columns 1 through 2 1.0000 0 0 -0.1095 + 0.1156i 0 0 0 0 Columns 3 through 4 0 0 0 0 -0.1095 - 0.1156i 0 0 -0.1039 v=V(:,1)' v = 0.4733 0.4530 0.7080 0.2635 v*P ans = 0.4733 0.4530 0.7080 0.2635 sum(v) ans = 1.8979 norm(v) ans = 1 v=v/sum(v) v = 0.2494 0.2387 0.3731 0.1388 sum(v) ans = 1 eig([0,1;1,0]) ans = -1 1 P=randstoc(4) P = 0.2829 0.3127 0.2073 0.1970 0.1563 0.2151 0.2908 0.3378 0.3572 0.0862 0.1543 0.4023 0.1511 0.1558 0.5156 0.1774 v=invariantPotenze(P,1e-6,100) v = 0.2447 0.1848 0.2928 0.2777 [v,iter]=invariantPotenze(P,1e-6,100) v = 0.2447 0.1848 0.2928 0.2777 iter = 12 v*P ans = 0.2447 0.1848 0.2928 0.2777 diary off