Dynamics of piecewise linear maps and sets of nonnegative matrices
نویسنده
چکیده
We consider maps fK(v) = minA∈K Av and gK(v) = maxA∈KAv, where K is a finite set of nonnegative matrices and by “min” and “max” we mean component-wise minimum and maximum. We transfer known results about properties of gK to fK. In particular we show existence of nonnegative generalized eigenvectors of fK, give necessary and sufficient conditions for existence of strictly positive eigenvector of fK, study dynamics of fK on the positive cone. We show the existence and construct matrices A and B, possibly not in K, such that f K (v) ∼ Av and g K (v) ∼ Bv for any strictly positive vector v.
منابع مشابه
Dynamics of piecewise linear maps and sets of nonnegative matrices I . Bondarenko December 2 , 2008
We consider functions f v = min A∈K Av and gv = max A∈K Av, where K is a finite set of nonnegative matrices and by " min " and " max " we mean coordinate-wise minimum and maximum. We transfer known results about properties of g to f. In particular we show existence of nonnegative generalized eigenvectors for f , give necessary and sufficient conditions for existence of strictly positive eigenve...
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