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Erschienen in:
2007 | OriginalPaper | Buchkapitel
The Jordan Theorem
Erschienen in: Algebraic Multiplicity of Eigenvalues of Linear Operators
Verlag: Birkhäuser Basel
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In this chapter we prove the Jordan theorem, a pivotal result in mathematics, which establishes that, for every
$$ A \in \mathcal{M}_N \left( \mathbb{C} \right) $$
, the space ℂ
N
decomposes as the direct sum of the ascent generalized eigenspaces associated with each of the eigenvalues of
A
. Then, by choosing an appropriate basis in each of the ascent generalized eigenspaces, the Jordan canonical form of
A
is constructed. These bases are chosen in order to attain a similar matrix to
A
with a maximum number of zeros.