Notes on the Structure of Linear Transformations
نویسنده
چکیده
The goal of these notes is to give an accessible introduction to the structure theory of linear transformations. We want to develop enough of the theory for use in differential equations, with only basic linear algebra as a prerequisite. In a following set of notes, we will show how these results can be applied to differential equations. In the rest of the section, we will cover some topics that will be useful tools for the final results and which may be unfamiliar to the reader. In order to deal with results over both the real and complex numbers, we will use the symbol K to mean either R or C. Thus, a statement made in terms of K is supposed to hold in both the real and complex cases. We will not use boldface notation for vectors in these notes.
منابع مشابه
Addendum 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...
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