A=matrix([[0,1/2,1/2],[1/2,0,1/2],[1/2,1/2,0]]); B=matrix([[0,0,0],[0,1,0],[0,0,1]]);C=A*B; Id=matrix.identity(3); x0=matrix([[1],[0],[0]]); At=A.transpose(); At*x0 At*B*At*x0;At^3*x0;At^4*x0;
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A=matrix([[0, 1/3,1/3,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1/3], [1/3, 0,1/3,1/3,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [1/3, 1/3,0,0,1/3,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 1/3,0,0,1/3,1/3, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,1/3,1/3,0,1/3, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,1/4,1/4,0, 1/4,1/4,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,1/3, 0,0,1/3,0,0, 0,0,0,0,0, 0,1/3,0,0,0, 0], [0, 0,0,0,0,1/3, 0,0,1/3,1/3,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 1/4,1/4,0,0,0, 0,0,0,0,1/4, 1/4,0,0,0,0, 0], [0, 0,0,0,0,0, 0,1/3,0,0,1/3, 1/3,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,1/3,0, 1/3,1/3,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,1/3,1/3, 0,0,1/3,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,1/3, 0,0,1/3,1/3,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 1/3,1/3,0,1/3,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,1/3,1/3,0,1/3, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,1/3,0,0, 0,0,0,1/3,0, 1/3,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,1/3,0,0, 0,0,0,0,1/3, 0,1/3,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1/3,0,1/3,0,1/3, 0], [0, 0,0,0,0,0, 1/3,0,0,0,0, 0,0,0,0,0, 0,1/3,0,1/3,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,1/3,0,1/3, 1/3], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,1/3,0,1/3,0, 1/3], [1/3, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,1/3,1/3, 0]]); Idf=matrix([[1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,1,0,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,1,0,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0], [0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1]]); xf=matrix([0, 0,0,0,0,0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0]); x0=xf.transpose(); At=A.transpose(); Id22=matrix.identity(22);
L=Idf*At; B=(Id22-L); show(B.det()); l=xf*At*(L*B.inverse()^2+B.inverse())*x0; show(n(l));
15496819561419025
(16.7160021845986)