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%%% Matlab lecture 11: Linear algebra with matlab and application
%%% to solving coupled linear  ODEs
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% Suppose we want to solve X_dot = A X, with the following matrix A:
A = [1, -1, 0; 1, 2, 1; -1, 1, 0]
%and with the collowing initial conditions:
X0 = [0.1; -0.1; 0.02]

% Let's diagonalize the matrix A: 
[P,D] = eig(A)

%Since X=PY,  the initial  values in term of Y are: 
Y0 = inv(P) * X0;

%Now, say you want to know X(t) at t=0.3 s for instance: 
t	= 0.3;
d	= diag(D);	% extracts the main diagonal of D
Y	= Y0 .* exp(d*t);
X	= P*Y		% There you go...