Re: bound on eigenvalues...

José Carlos Santos wrote: 
The eigenvalues are the roots of the characteristic polynomial, which is
P(x) = -x^3 + a x^2 + b x + c, with a = 0.501, b = -0.024089, and
c = 0.0000524046. Since it's a third degree polynomial, it can't have
more than three roots. Now, since P(0) = 0.0000524046, P(0.05) =
-0.0000245449, P(0.1) = 0.00165351, P(0.4) = 0.00657681, and P(0.5) =
-0.0117421, there must be a root between 0 and 0.1, a second one between
0.1 and 0.4, and a third one between 0.4 and 0.5. This proves that all
roots are smaller than 0.5.


But I think he *meant* to write that there must be a root
between 0 and 0.05, a second one between 0.05 and 0.1,
and a third one between 0.4  and 0.5, since that's how the
sign changes go.
.