Ela a Note on Power Bounded Matrices
نویسندگان
چکیده
We say A is convergent to the matrix X = [xij ] if the sequences (A )ij converge to xij as k → ∞. A matrix is convergent if it is convergent to some matrix. This is a special case of convergence as defined in [4, Definition 10.1], for the matrix sequence {A,A, A, . . . }. In particular, we say A is zero convergent when A is convergent to the zero matrix. We distinguish between convergence and zero convergence (i.e., convergence to the zero matrix) of A. Needless to say, A can be power bounded without being convergent, as seen from the example A = −I.
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