Символическая ошибка собственных значений Matlab

Question

Я пытаюсь найти собственные векторы символической матрицы вращения 3x3 в MATLAB, она работает для некоторых входов, но не для всех, например:

A =
[ cos(q), -sin(q), 0]
[ sin(q), cos(q), 0]
[ 0, 0, 1]

[V,lambda]=eig(A)

V =
[ 0, -i, i]
[ 0, 1, 1]
[ 1, 0, 0]

lambda =
[ 1, 0, 0]
[ 0, cos(q) - sin(q)*i, 0]
[ 0, 0, cos(q) + sin(q)*i]

, это работает нормально, однако, если япопробуйте что-то, что не является вращением вокруг оси единицы (x, y, z), я получаю следующую ошибку:

A =
[ cos(q), -sin(q), 0]
[ 0, 0, -1]
[ sin(q), cos(q), 0]

>> [V,lambda]=eig(A)
Warning: basis of eigenspace for eigenvalue cos(q)/3 - (cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 +
(cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3)/2 + (cos(q)/3 - cos(q)^2/9)/(2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 +
((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/... [linalg::eigenvectors] 
??? Error using ==> mupadmex
Error in MuPAD command: Unable to find explicit eigenvectors.

Error in ==> sym.sym>sym.mupadmexnout at 2003
out = mupadmex(fcn,args{:});

Error in ==> sym.eig at 68
[V,D,p] = mupadmexnout('mllib::eigenvectors',A);

Я использую собственные значения, чтобы найти ось вращения матрицы, иМне нужно использовать его для гораздо более сложных систем

Любая помощь будет оценена.Спасибо

Answer 1

Я не могу воспроизвести ошибку (проверено на MATLAB R2010b):

syms q
A = [cos(q) -sin(q) 0 ; 0 0 -1 ; sin(q) cos(q) 0]
[V,lambda] = eig(A)

Я получаю следующий (довольно длинный) результат:

A =
[ cos(q), -sin(q),  0]
[      0,       0, -1]
[ sin(q),  cos(q),  0]

V =
[ (3*cos(q)^2 + 4*cos(q)^3 + cos(q)^4 + 27*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(4/3) + 9*cos(q)*sin(q)^2 + 9*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) - 6*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 9*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 2*cos(q)^3*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 18*cos(q)*(cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))/(3*sin(q)*(cos(q)^2 - 3*cos(q) + 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 3*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3))*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)), (3*cos(q)^2 - 27*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(4/3)*i + 4*cos(q)^3 + cos(q)^4 + 27*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(4/3) + 9*cos(q)*sin(q)^2 - 18*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) - 6*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) - 18*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 2*cos(q)^3*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 3*3^(1/2)*cos(q)^2*i + 4*3^(1/2)*cos(q)^3*i + 3^(1/2)*cos(q)^4*i + 18*cos(q)*(cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2) + 6*3^(1/2)*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*i - 2*3^(1/2)*cos(q)^3*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*i + 18*3^(1/2)*cos(q)*(cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2)*i + 9*3^(1/2)*cos(q)*sin(q)^2*i)/(3*sin(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*(cos(q)^2 + 9*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3)*i - 3*cos(q) + 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) - 6*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 3*3^(1/2)*cos(q)*i - 3^(1/2)*cos(q)^2*i)), -(27*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(4/3)*i + 3*cos(q)^2 + 4*cos(q)^3 + cos(q)^4 + 27*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(4/3) + 9*cos(q)*sin(q)^2 - 18*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) - 6*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) - 18*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 2*cos(q)^3*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) - 3*3^(1/2)*cos(q)^2*i - 4*3^(1/2)*cos(q)^3*i - 3^(1/2)*cos(q)^4*i + 18*cos(q)*(cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2) - 6*3^(1/2)*cos(q)^2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*i + 2*3^(1/2)*cos(q)^3*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*i - 18*3^(1/2)*cos(q)*(cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2)*i - 9*3^(1/2)*cos(q)*sin(q)^2*i)/(3*sin(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)*(3*cos(q) + 9*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3)*i - cos(q)^2 - 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 6*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 3*3^(1/2)*cos(q)*i - 3^(1/2)*cos(q)^2*i))]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               -(9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3))/(cos(q)^2 - 3*cos(q) + 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 3*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3)),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             (18*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3))/(cos(q)^2 + 9*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3)*i - 3*cos(q) + 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) - 6*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 3*3^(1/2)*cos(q)*i - 3^(1/2)*cos(q)^2*i),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             -(18*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3))/(3*cos(q) + 9*3^(1/2)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3)*i - cos(q)^2 - 9*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(2/3) + 6*cos(q)*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + (cos(q)^5/27 + (2*cos(q)^4)/27 + (cos(q)^3*sin(q)^2)/27 + cos(q)^3/27 + (cos(q)^2*sin(q)^2)/3 + sin(q)^4/4)^(1/2))^(1/3) + 3*3^(1/2)*cos(q)*i - 3^(1/2)*cos(q)^2*i)]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   1,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1]

lambda =
[ cos(q)/3 + (cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3) - (cos(q)/3 - cos(q)^2/9)/(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3),                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              0,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              0]
[                                                                                                                                                                                                                                                                                                0, cos(q)/3 - (cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3)/2 + (cos(q)/3 - cos(q)^2/9)/(2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3)) - (3^(1/2)*((cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3) + (cos(q)/3 - cos(q)^2/9)/(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3))*i)/2,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              0]
[                                                                                                                                                                                                                                                                                                0,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              0, cos(q)/3 - (cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3)/2 + (cos(q)/3 - cos(q)^2/9)/(2*(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3)) + (3^(1/2)*((cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3) + (cos(q)/3 - cos(q)^2/9)/(cos(q)^2/3 + cos(q)^3/27 + sin(q)^2/2 + ((cos(q)/3 - cos(q)^2/9)^3 + (cos(q)^3/27 + cos(q)^2/3 + sin(q)^2/2)^2)^(1/2))^(1/3))*i)/2]

Answer 2

Проблемный пример, который вы привели, не является общей матрицей вращения, 1 не является собственным значением. Подробнее здесь http://en.wikipedia.org/wiki/Rotation_matrix. Это не должно влиять на функцию matlab, однако вам гарантируется базис обобщенных собственных векторов над комплексными числами. У вас есть еще информация об ошибке? Я заметил некоторые вызовы функций на основе симметричных матриц. Вы пытались вызвать eig с опцией 'qz' для явного вызова алгоритма на несимметричной основе?