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Mathematics-Online lexicon:

Jordan Form

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A square matrix $ A$ can be brought to block diagonal form by a similarity transformation

$\displaystyle J = \left(\begin{array}{ccc} J_1 & & 0 \\ & \ddots & \\ 0 & & J_k \end{array}\right) = Q^{-1} A Q\,. $

Here the Jordan blocks have the form

$\displaystyle J_i = \left(\begin{array}{ccccc} \lambda_i & 1 & & & 0 \\ 0 & \... ...ts & \\ & & & \lambda_i & 1 \\ 0 & & & & \lambda_i \end{array}\right) \,, $

where $ \lambda_i$ is an eigenvalue of $ A$.
[Examples] [Links]
  automatically generated 5/17/2011