%% Study plane rotations with the Symbolic Math Toolbox

%  Copyright 1993-2002 The MathWorks, Inc. 
%  $Revision: 1.8.4.1 $  $Date: 2004/08/20 20:06:38 $

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% Create a symbolic variable named t.

t = sym('t')

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% Create a 2-by-2 matrix representing a plane rotation through an angle t.

G = [ cos(t) sin(t); -sin(t) cos(t)]

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% Compute the matrix product of G with itself.

G*G

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% This should represent a rotation through an angle of 2*t.
% Simplification using trigonometric identities is necessary.

ans = simple(ans)

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% G is an orthogonal matrix; its tranpose is its inverse.

G.'*G

ans = simple(ans)

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% What are the eigenvalues of G?

e = eig(G)

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% Repeatedly apply the simplification rules.

e, for k = 1:4, e = simple(e), end