منابع مشابه
On the Infinite Products of Matrices
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 کاملInfinite products and paracontracting matrices
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...
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...
متن کاملCompactification of a set of matrices with convergent infinite products
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...
متن کاملInfinite Products of Nonnegative 2× 2 Matrices by Nonnegative Vectors
Given a finite set {M0, . . . ,Md−1} of nonnegative 2× 2 matrices and a nonnegative column-vector V , we associate to each (ωn) ∈ {0, . . . , d− 1}N the sequence of the column-vectors Mω1 . . .MωnV ‖Mω1 . . .MωnV ‖ . We give the necessary and sufficient condition on the matrices Mk and the vector V for this sequence to converge for all (ωn) ∈ {0, . . . , d− 1}N such that ∀n, Mω1 . . .MωnV 6= ( ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2012
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2012.25050