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 ℂN 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.


Characteristic Polynomial Hermitian Matrix Jordan Block Linear Manifold Algebraic Multiplicity 
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© Birkhäuser Verlag AG 2007

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