Equivalent Characterizations of Periodical Invariant Subspaces
نویسندگان
چکیده
This paper mainly treats of the interconnections between the periodic Schur form and its associated periodical deflating subspaces. We establish some equivalent statements of the periodic Schur decomposition for regular periodic matrix pairs. Based on these equivalences, we define the eigenspaces for regular periodic matrix pairs, and point out the corresponding eigenvalues inherited from a given eigenspace sequence. We express the set of eigenvalues associated with a given eigenspace sequence in terms of various forms such as the corresponding periodic Schur form and the algebraic form of an eigenspace sequence. Besides, we connect the results with classical ones when all the component matrices are invertible.
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