Sets of matrices all infinite products of which converge
نویسندگان
چکیده
منابع مشابه
Sets 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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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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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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Let $mathcal{F}$ be an field of zero characteristic and $N_{infty}(mathcal{F})$ be the algebra of infinite strictly upper triangular matrices with entries in $mathcal{F}$, and $f:N_{infty}(mathcal{F})rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $N_{infty }(mathcal{F})$; that is, a map satisfying that $f([X,Y])=[f(X),Y]$ for all $X,Yin N_{infty}(mathcal{F})...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90012-y