Legacy Documentation

8.3 Jordan Canonical (Modal) Form

Finding the Jordan canonical form.

Let us create a diagonal matrix.

In[13]:=

Out[13]=

Here is some nonsingular matrix.

In[14]:=

Out[14]=

This creates a matrix with the predefined set of eigenvalues.

In[15]:=

Out[15]=

We use the previous matrix as matrix in our test state-space object ss.

In[16]:=

Out[16]=

In[17]:=

Out[17]=

This finds the Jordan canonical form of the preceding system.

In[18]:=

Out[18]=

In the case of an exact input system, JordanCanonicalForm relies on the built-in function JordanDecomposition; otherwise the eigenvalue decomposition is used. The latter method may lead to significant numerical errors if eigenvalues happen to be multiple.