% Matlab script to solve Example 2.1.1
tau = [-40, -10; -10, -60];               % stress tensor
nhat = [1/sqrt(2); 1/sqrt(2)]             % fault normal unit vector
trac = tau * nhat                         % traction across fault
trac_norm = dot(trac, nhat)               % normal stress on fault
fhat = [1/sqrt(2); -1/sqrt(2)]            % fault parallel unit vector
trac_shear = dot(trac, fhat)              % shear stress on fault


% Matlab script to solve Example 2.1.3
tau = [-40, -10; -10, -60];
[N, Lam] = eig(tau)    % gives eigenvectors as columns of N, eigenvalues on diagonal of Lam
angle = atan(N(2,1)/N(1,1))*180/pi    % compute angle of 1st eigenvector wrt x-axis and convert to degrees
taur = N' * tau * N    % compute rotated stress tensor