符号特征值Matlab错误

问题描述

| 我正在尝试在MATLAB中查找符号3x3旋转矩阵的特征向量，它似乎适用于某些输入，但并非全部输入，例如：

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

[V,lambda]=eig(A)

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

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

这工作正常，但是，如果我尝试的操作不是围绕单位轴（x，y，z）旋转，则会出现以下错误：

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

我正在使用特征值来查找矩阵的旋转轴，因此我需要将其用于更复杂的系统 任何帮助，将不胜感激。 谢谢     

解决方法

        我无法重现该错误（已在MATLAB R2010b上测试）：

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

我得到以下结果（相当长）：

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

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,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,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]

    ,        您给出的有问题的示例不是通用旋转矩阵，1不是特征值。在此处查看更多信息http://en.wikipedia.org/wiki/Rotation_matrix。这不应该影响matlab函数，但是，可以保证您是复数上广义特征向量的基础。您是否有关于该错误的更多信息？我注意到一些对基于对称矩阵的函数的调用，您是否尝试过使用带有选项'qz \'的eig来显式调用基于非对称算法的算法？