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8. Calculating the switch dimension
This calculation is used to compute the dimension of orbits. The method consists in finding the dimension of its commutant for a nilpotent matrix, as this is sufficient given the following lemma.
Lemma 2. If
is a block-diagonal matrix verifying that the characteristic polynomials of A and B are prime to each other, then the matrices that commute with M are block-diagonal, i.e.
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Calculating the switch dimension
Simultaneous reduction
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