Genericness of solution to N-dimensional polynomial matrix equation XA=I

It is shown that the solution to N-dimensional polynomial matrix equation XA=I, dim A=n*m is generic if n>or=m+N, and nongeneric in other cases. The author shows how to apply this result to equations with structured matrices A. An example of application is given: c-observability and c-reconstructability of a 2-D general state-space model are generic if a system has more than one output.<
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