- #1

- 315

- 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 thats because i know what this matrix is... but if i'll see some matrix with different values then this roaming around.... i dont know what i'll do, i dont 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 thats because i know what this matrix is... but if i'll see some matrix with different values then this roaming around.... i dont know what i'll do, i dont 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: