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7. Special families of matrices. Matrices of class δ
The subspace Ker M 2 has a dimension that varies between two bounds: the dimension of Ker A and its double. Matrices such as Ker A = Ker A 2
and matrices such as
dim(Ker A 2 ) = 2 dim(Ker A)
form two families that deserve special attention. The following propositions give some characteristic properties of one or other of these two families. Keep in mind the exact sequence
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Special families of matrices. Matrices of class δ
Calculating the switch dimension
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