# The Jordan Theorem

Chapter

## Abstract

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.

## Keywords

Characteristic Polynomial Hermitian Matrix Jordan Block Linear Manifold Algebraic Multiplicity
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## Copyright information

© Birkhäuser Verlag AG 2007