MatLab Instructions (1)

• Computing Vector Norms:
  Type help norm to learn how to compute 1-norm, 2-norm, p-norm and infinity-norm for a given vector using MatLab m-function norm. The following is the m-file which computes 1-norm, 2-norm and infinity-norm of vector x_k-x where x_k=[ksin(1/k); 3+1/k; cos(k)/e^k]. You recieved a hard copy of the graph in class last Thursday.

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    clf
    clear
    n=input('input n = ');
    vsol=[1;3;0];
    for i=1:n
      vv(1,i)=i*sin(1/i);
      vv(2,i)=3+1/i;
      vv(3,i)=cos(i)/exp(i);
      difv(:,i)=vv(:,i)-vsol;
      nor1(i,1)=norm(difv(:,i),1);
      nor2(i,1)=norm(difv(:,i),2);
      norinf(i,1)=norm(difv(:,i),inf);
    end;
    semilogy(nor1,'-.')
    hold
    semilogy(nor2,':')
    semilogy(norinf,'--')
    hold off
    title('||x(k)-x||, where x(k)=[k*sin(1/k) 3+1/k cos(k)/e^k], x=[1;3;0]')
    xlabel('index k')
    ylabel('log(||x(k)-x||)')
    text(3,1,'-.-. 1-norm, .... 2-norm, ---- infinity-norm')
  

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• Computing Matrix Norms:
  Type help norm to learn how to compute 1-norm, 2-norm, and infinity-norm for a given matrix using MatLab m-function norm.
  
• Computing Eigenvalues and Eigenvectors:
  Type help eig to learn how to compute eigenvalues of eigenvectors of a given matrix A. To determine the number of linearly independent eigenvectors, you may use MatLab m-function rank. Recall that the rank of a given matrix V is n iff n column vectors (or n row vectors) of V are linearly independent. Let [V D]=eig(A). Since columns of V are eigenvectors of A, the rank of V = # of linearly independent eigenvectors.