The "principle eigenvalue" is the one that is largest in absolute value.
Studying for a test
a) show that the principle eigenfuntion is not sign changing
b) show all the other eigenfunctions are sign changing.
i'm not sure what this mean or what i meant by "princple"
can anone point me in the right direction?
i have in my notes that all of the eigenvalues are positive
wouldn't all of the eigenfunctions also be positive?
my professor mentioned something in class about the fact that
Int(u_1*u_m*rho dx)=0
>>> u_1>0, rho>0
>>> u_m must be sign changing
i think that what he said is pretty much all of it, but i really don't know what it means and i don't have anyone around that is in pde with me to ask... i have a test on friday... HELP
i'm not sure why these questions are relevant
i am under the impression that if something is sign changing it will cancel to zero when you comupet the integral, but then the whole integral would be zero....
and i always get confused when i get a lot of zeros, because it normally means i have made a mistake...