- #1
fargoth
- 320
- 6
is there any trick for finding the eigenvalues and vectors for this kind of matrix?
[tex]
\left(
\begin{array}{ccccc}
0 & 1 & 0 & 0 & 0 \\
1 & 0 & \sqrt{\frac{3}{2} & 0 & 0 \\
0 & \sqrt{\frac{3}{2} & 0 & \sqrt{\frac{3}{2} & 0 \\
0 & 0 & \sqrt{\frac{3}{2} & 0 & 1 \\
0 & 0 & 0 & 1 & 0 \\
\end{array}
\right)
[/tex]
i mean, i can tell the eigenvalues are 2,1,0,-1,-2... and i can tell the eigenvectors would have a=e and b=d... but that's because i know what this matrix is... but if i'll see some matrix with different values then this roaming around... i don't know what i'll do, i don't think trying to solve the standard polynom of it is a good idea... and after knowing the eigenvalues one has to solve the set of equations to find the eigenvectors -yuck!-
[tex]
\left(
\begin{array}{ccccc}
0 & 1 & 0 & 0 & 0 \\
1 & 0 & \sqrt{\frac{3}{2} & 0 & 0 \\
0 & \sqrt{\frac{3}{2} & 0 & \sqrt{\frac{3}{2} & 0 \\
0 & 0 & \sqrt{\frac{3}{2} & 0 & 1 \\
0 & 0 & 0 & 1 & 0 \\
\end{array}
\right)
[/tex]
i mean, i can tell the eigenvalues are 2,1,0,-1,-2... and i can tell the eigenvectors would have a=e and b=d... but that's because i know what this matrix is... but if i'll see some matrix with different values then this roaming around... i don't know what i'll do, i don't think trying to solve the standard polynom of it is a good idea... and after knowing the eigenvalues one has to solve the set of equations to find the eigenvectors -yuck!-
Last edited: