Invertibly convergent infinite products of matrices
نویسندگان
چکیده
منابع مشابه
Invertibly convergent in nite products of matrices
The standard de nition of convergence of an in nite product of scalars is extended to the in nite product P= n=1Bn of k × k matrices; that is, P is convergent according to the de nition given here if and only if there is an integer N such that Bn is invertible for n¿N and P= limn→∞ m=NBm is invertible. A family of su cient conditions for this kind of convergence is given, along with examples sh...
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We generalize and unify some aspects of the work of I. Daubechies, J.C. Lagarias [Linear Algebra Appl. 162 (1992) 227–263] on a set R of matrices with right-convergent-products (RCPs). We show that most properties of an RCP set R pass on to its compactification R (i.e., its closure in the matrix space). Results on finite RCP sets generally hold for compact RCP sets, among which is the existence...
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In [Linear Algebra Appl., 161:227{263, 1992] the LCP-property of a nite set of square complex matrices was introduced and studied. A set is an LCP-set if all left in nite products formed from matrices in are convergent. It was shown earlier in [Linear Algebra Appl., 130:65{82, 1990] that a set paracontracting with respect to a xed norm is an LCP-set. Here a converse statement is proved: If is a...
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In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product of matrices chosen from a possibly infinite set of matrices 0 i i P , j M P j J k i P 0 k k i converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also ...
متن کاملSets of Matrices All Infinite Products of Which Converge
An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if all infinite products with each element drawn from Z converge. Such sets of matrices arise in constructing self-similar objects like von Koch’s snowflake curve, in various interpolation schemes, in construc...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00191-5