- #1
psholtz
- 136
- 0
I'm reading from Wikipedia:
I thought linear operators always had eigenvalues, since you could always form a characteristic equation for the corresponding matrix and solve it?
Is that not the case? Are there linear operators that don't have eigenvalues?
The spectrum of any bounded symmetric operator is real; in particular all its eigenvalues are real, although a symmetric operator may have no eigenvalues.
http://en.wikipedia.org/wiki/Self-adjoint_operator
I thought linear operators always had eigenvalues, since you could always form a characteristic equation for the corresponding matrix and solve it?
Is that not the case? Are there linear operators that don't have eigenvalues?