My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By whitegreen
Reply
 
LinkBack Thread Tools Display Modes
August 13th, 2016, 03:08 AM   #1
Newbie
 
Joined: Oct 2014
From: China

Posts: 12
Thanks: 2

eigenvectors of matrix of eigenvectors entries

The standard method (Characteristic polynomial) for the eigenvectors of
$$
\begin{bmatrix}
-\sin(y)\cos(z) & \sin(y)\cos(x) & \sin(x)\cos(z) \\
\sin(y)\cos(x) & -\sin(z)\cos(x) & \sin(z)\cos(y) \\
\sin(x)\cos(z) & \sin(z)\cos(y) & -\sin(x)\cos(y) \\
\end{bmatrix}
$$
leads to a complicated polynomial (degree 3) that cannot be easily solved.
Is there any other methods for the eigenvectors of this particular matrix (there are a lot of symmetry inside)?
Thanks from 123qwerty
whitegreen is offline  
 
August 17th, 2016, 07:55 AM   #2
Member
 
Rebesques's Avatar
 
Joined: Aug 2007

Posts: 42
Thanks: 4

Three positive eigenvalues (expected, as the matrix is symmetric)


First: (cos(z)*sin(y))/3 - (cos(x)*sin(z))/3 - (cos(y)*sin(x))/3 + ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + \\(cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)/(((((cos(y)*sin(x) + cos(x)*sin(z) - \\
cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + \\(cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 \\ + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - \\(cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*\\(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) +\\ cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3) +\\ (((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 +\\ (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - \\(3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 -\\ (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*\\(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + \\cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3)


Second: (cos(z)*sin(y))/3 - (cos(x)*sin(z))/3 - (cos(y)*sin(x))/3 - (3^(1/2)*(((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)/(((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3) - (((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3))*i)/2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)/(2*(((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3)) - (((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3)/2

Third: (cos(z)*sin(y))/3 - (cos(x)*sin(z))/3 - (cos(y)*sin(x))/3 + (3^(1/2)*(((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)/(((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3) - (((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3))*i)/2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)/(2*(((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3)) - (((((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 - (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 + (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 - (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^2 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^2/9 + (cos(x)^2*sin(y)^2)/3 + (cos(z)^2*sin(x)^2)/3 + (cos(y)^2*sin(z)^2)/3 - (cos(x)*cos(y)*sin(x)*sin(z))/3 + (cos(y)*cos(z)*sin(x)*sin(y))/3 + (cos(x)*cos(z)*sin(y)*sin(z))/3)^3)^(1/2) - (cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))^3/27 - ((cos(y)*sin(x) + cos(x)*sin(z) - cos(z)*sin(y))*(cos(x)^2*sin(y)^2 + cos(z)^2*sin(x)^2 + cos(y)^2*sin(z)^2 - cos(x)*cos(y)*sin(x)*sin(z) + cos(y)*cos(z)*sin(x)*sin(y) + cos(x)*cos(z)*sin(y)*sin(z)))/6 + (cos(x)^2*cos(y)*sin(x)*sin(y)^2)/2 + (cos(x)*cos(z)^2*sin(x)^2*sin(z))/2 - (cos(y)^2*cos(z)*sin(y)*sin(z)^2)/2 + (3*cos(x)*cos(y)*cos(z)*sin(x)*sin(y)*sin(z))/2)^(1/3)/2

Last edited by Rebesques; August 17th, 2016 at 07:59 AM.
Rebesques is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
eigenvectors, entries, matrix



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Eigenvectors harley05 Calculus 1 June 10th, 2014 06:18 AM
Matrix 2x2 - eigenvectors + eigenvalues tomiojap Linear Algebra 1 March 20th, 2013 04:02 PM
Eigenvectors happygolucky88 Linear Algebra 1 October 18th, 2009 02:13 PM
Eigenvectors Matt Linear Algebra 0 October 10th, 2009 04:27 PM
Eigenvectors of Hessian Matrix asmatic Linear Algebra 0 July 31st, 2009 11:51 AM





Copyright © 2018 My Math Forum. All rights reserved.