Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
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Abstract:
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
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infinite-dimensional versions of the primary, cyclic and jordan decompositions
the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
full textAddendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
full textaddendum to: "infinite-dimensional versions of the primary, cyclic and jordan decompositions", by m. radjabalipour
in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...
full textinfinite dimensional garch models
مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...
15 صفحه اولJordan decompositions
If F is an algebraically closed field, any element in M n (F) is similar to a sum of a diagonal matrix and a nilpotent matrix whose non-zero entries are all 1, just above the diagonal. Something similar is true for elements of an arbitrary affine algebraic group as well as its Lie algebra. That's what this essay will attempt to explain. I begin with a very elementary account of what happens for...
full textThe Classification of Some Infinite Jordan Groups
WHEN we speak of a 'back and forth' construction for proving the isomorphism of two countable structures we call to mind the famous theorem of Cantor that any countable dense linearly ordered set without end-points is order-isomorphic to Q. Cantor's own proof requires only the 'going forth' part of the construction, however, and Adrian Mathias, on noticing this, asked for a classification of th...
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Journal title
volume 41 issue Issue 7 (Special Issue)
pages 175- 183
publication date 2015-12-01
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