Matrices similar on a Zariski - open set
نویسنده
چکیده
1. Introduction ,(1.1) Let A, B be n x n matrices whose elements are functions holomorphic in a connected open subset V of the complex plane. The matrices A, Bare called pointwise similar on V if for each XE V there exists a non-singular n x n matrix C x with complex elements such that B(x) = C;;l A (x) Cx' They are holomorphically similar on V if there exists a matrix C of functions holomorphic on V for which B(x)=C(X)-lA(x) C(x), for all XEV. WASOW [5] gives two related criteria (one due to OSTROWSKI) to determine when pointwise similarity on a neighborhood V of Xo implies holomorphic similarity on a (possibly smaller) neighborhood of Xo'
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