- #1
- 753
- 2
Homework Statement
What kind of conditions do eigenvalues impose to ensure periodicity?
Is it plausible to say that irrational multiples of eigenvalues imply no harmonic oscillations, if so why?
Now that makes more sense. It also looks like a hard question. How about a=1, b=0, c=1? Is that good enough? What's this for anyway?[tex]
\left[\begin{array}{cccc}0 & -a & 0 & 0 \\ -a & 0 & -b & 0 \\ 0 & -b & 0 & -c \\ 0 & 0 & -c & 0\end{array}\right]
[/tex]
For any fixed a, I want to find b and c in terms of a such that lambda_i / lambda_ j is a rational number for every i,j=1,2,3,4 .
See, before I was working with
[tex]
\left[\begin{array}{cccc}0 & -a & 0 & 0 \\ -a & 0 & -a & 0 \\ 0 & -a & 0 & -a \\ 0 & 0 & -a & 0\end{array}\right]
[/tex]
But that gave me irrational e-values if I put it into Maple and I don't want that.