%File: decompose

function y=select(P)

%SELECT expresses a diagonalizable state

% matrix P in terms of

% lambda1, A1

% lambda2, A2, etc.

% If P has m distinct eigenvalues, SELECT returns

% m+1 matrices. The first matrix is the diagonal

% matrix containing all the eigenvalues.

% The other matrices are A1, A2, ..., Am.

m = size(P,1); %determine the number of rows, or columns.

[X,D] = eig(P); % determine eigenvectors and eigenvalues

X_inv = inv(X);

y(:,:,1) = D; % first matrix is D

for i=1:m,

sel = zeros(m);

sel(i,i) = 1; % sel is a matrix to deterine A_i

y(:,:,i+1) = X*sel*X_inv;

end