On pointwise and analytic similarity of matrices |
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| Authors: | Shmuel Friedland |
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| Institution: | (1) Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, U.S.A.;(2) Present address: Hebrew University of Jerusalem, Jerusalem, Israel |
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| Abstract: | LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 |
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| Keywords: | |
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