% Exercise matrices

% Study A below in EigTool for several values of N
% Take for example N = 5, 10, 25, 50
% Also, do your own plots and determine the slope of
% norm(exp(tA)) for t small and large

N=50;
row=[0 2*ones(1,N-1)];
col=zeros(1,N);
A=toeplitz(col,row);

% Same questions for a Jordan block nilpotent matrix

L=10;
r=[0 1 zeros(1,L-2)];
c=zeros(1,L);
J=toeplitz(c,r);


% For the two matrices below compute the pseudospectra,
% field of values etc. in EigTool

X=[-5 4 4;
    0 -2-2*i 4;
    0 0 -3+i];

XX=[-5 0 0;
    0 -2-2*i 0;
    0 0 -3+i];