spectrum of
Let be an endomorphism of the vector space
over a field . Denote by the spectrum
of . Then we have:
Theorem 1.
Theorem 1 is equivalent to:
Theorem 2.
is a spectral value of if and only if is a spectral value of .
Proof of Theorem 2.
Note that
and thus is invertible if and only if
is invertible. Equivalently,
is a spectral value of iff is a
spectral value of , as desired.
∎
Title | spectrum of |
---|---|
Canonical name | SpectrumOfAmuI |
Date of creation | 2013-03-22 15:32:49 |
Last modified on | 2013-03-22 15:32:49 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 9 |
Author | PrimeFan (13766) |
Entry type | Theorem |
Classification | msc 15A18 |
Related topic | SpectralValuesClassification |