ExampleJCF.m: HONHmo WP-NOOP %Example JCF from Lecture 13 A = [2,0,0,0,0,1,1, 0,3,0,0,0,0 -1,-3,1,1,0 0,3, 0,2,-1,1 0,1,0,0,0, 0,1,0,0,0,0,3, 0; 3 ,11 , 1,-2 ,0 ,-2, 4, 1] eig(A) lambda = 1; Wilambda = null(lambda*eye (8,8)-A,'r') W2lambda = null((lambda*eye(8,8)-A)^2, 'r') W3lambda = null((lambda*eye(8,8)-A)^3, 'r') ell = 1; d = 2; v12lambda = W2lambda(:,1) villambda = (A-lambda*eye(8,8))*v12 lambda Vilambda = [villambda, v121 ambda] ell = 2; d = 1; v21lambda = Wilambda(:,1) V2lambda = (v21lambda] Vlambda1 = [vilambda, v2lambda] lambda = 2; Wilambda = null(lambda*eye(8,8)-A, 'r') Vlambda2 = Wilambda; lambda = 3; Wilambda = null(lambda*eye (8,8)-A,'r') W2lambda = null((lambda*eye(8,8)-A)^2, 'r') W3lambda = 2*null((lambda*eye(8,8)-A)^3,''; W3lambda (:,1:2)=W21 ambda %multiplying with 2 to avoid fractions, changing first two columns to equal W2 lambda without changing the actual span (not necessary, just looks nicer) W4lambda = 2*null((lambda*eye(8,8)-A)-4,'r') %multiplying with 2 to avoid fractions rank([W3lambda, W41ambda]) ell = 1; d = 3; v13lambda = W3lambda(:,3) v12lambda = (A - lambda*eye(8,8)) *v131 ambda v11lambda = (A - lambda*eye(8,8)) *v121 ambda Vlambda3 = (v11lambda, v121 ambda, v13lambda] P = [Vlambda1, Vlambda2, Vlambda3] P^(-1)*A*P Computer assignment CHW9:25 Points (bonus) Adapt the matlab-script exampleJCF.m from the lecture available on Nestor to obtain a coordinate transformation which transforms the following matrix A to JCF [2 0 0 0 0 0 -1 2 0 0 0 0 0 0 1 0 0 0 1 0 1 3 0 1 -1 0 0 -1 1 0 -1] 0 0 -11 0 1 ExampleJCF.m: HONHmo WP-NOOP %Example JCF from Lecture 13 A = [2,0,0,0,0,1,1, 0,3,0,0,0,0 -1,-3,1,1,0 0,3, 0,2,-1,1 0,1,0,0,0, 0,1,0,0,0,0,3, 0; 3 ,11 , 1,-2 ,0 ,-2, 4, 1] eig(A) lambda = 1; Wilambda = null(lambda*eye (8,8)-A,'r') W2lambda = null((lambda*eye(8,8)-A)^2, 'r') W3lambda = null((lambda*eye(8,8)-A)^3, 'r') ell = 1; d = 2; v12lambda = W2lambda(:,1) villambda = (A-lambda*eye(8,8))*v12 lambda Vilambda = [villambda, v121 ambda] ell = 2; d = 1; v21lambda = Wilambda(:,1) V2lambda = (v21lambda] Vlambda1 = [vilambda, v2lambda] lambda = 2; Wilambda = null(lambda*eye(8,8)-A, 'r') Vlambda2 = Wilambda; lambda = 3; Wilambda = null(lambda*eye (8,8)-A,'r') W2lambda = null((lambda*eye(8,8)-A)^2, 'r') W3lambda = 2*null((lambda*eye(8,8)-A)^3,''; W3lambda (:,1:2)=W21 ambda %multiplying with 2 to avoid fractions, changing first two columns to equal W2 lambda without changing the actual span (not necessary, just looks nicer) W4lambda = 2*null((lambda*eye(8,8)-A)-4,'r') %multiplying with 2 to avoid fractions rank([W3lambda, W41ambda]) ell = 1; d = 3; v13lambda = W3lambda(:,3) v12lambda = (A - lambda*eye(8,8)) *v131 ambda v11lambda = (A - lambda*eye(8,8)) *v121 ambda Vlambda3 = (v11lambda, v121 ambda, v13lambda] P = [Vlambda1, Vlambda2, Vlambda3] P^(-1)*A*P Computer assignment CHW9:25 Points (bonus) Adapt the matlab-script exampleJCF.m from the lecture available on Nestor to obtain a coordinate transformation which transforms the following matrix A to JCF [2 0 0 0 0 0 -1 2 0 0 0 0 0 0 1 0 0 0 1 0 1 3 0 1 -1 0 0 -1 1 0 -1] 0 0 -11 0 1
