Similarity Transform

Transforming a matrix into an alternative form using a Transformation Matrix.

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A general state equation after doing a similarity transform with a Transition Matrix $T$

$$\begin{array}{rl}\dot{\bar{x}}& =TA{T}^{-1}\bar{x}+TBu\\ y& =C{T}^{-1}\bar{x}+Du\end{array}$$

Diagonal similarity transforms

Eigenvector/Values

Non diagonal similarity transforms

Jordan form