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initial version
A=matrix(SR,2,2,[3, -13, 5,1]) 
eig=A.eigenvectors_right();
eig

[(-8*I + 2, [(1, 8/13*I + 1/13)], 1), (8*I + 2, [(1, -8/13*I + 1/13)], 1)]

(Replace QQ by SR)