Certain essential concepts in linear algebra cannot be fully
explained in a first course. This is due to a lack of algebraic
background for most beginning students. On the other hand, these
concepts are taken for granted in most of the mathematical courses
at graduate school level. This book will provide a gentle guidance
for motivated students to fill the gap. It is not easy to find
other books fulfilling this purpose. This book is a suitable
textbook for a higher undergraduate course, as well as for a
graduate student's self-study. The introduction of set theory and
modules would be of particular interest to students who aspire to
becoming algebraists.Basically, there are two parts in this book.
One is to complete the discussion of bases and dimension in linear
algebra. In a first course, only the finite dimensional vector
spaces are treated, and in most textbooks, it will assume the
scalar field is the real number field. In this book, the general
case of arbitrary dimension and arbitrary scalar fields is
examined. To do so, an introduction to cardinality and Zorn's lemma
in set theory is presented in detail. The second part is to
complete the proof of canonical forms for linear endomorphisms and
matrices. For this, a generalization of vector spaces, and the most
fundamental results regarding modules are introduced to readers.
This will provide the natural entrance into a full understanding of
matrices. Tensor product of modules are also briefly discussed.
General
| Imprint: |
World Scientific Publishing Co Pte Ltd
|
| Country of origin: |
Singapore |
| Release date: |
2024 |
| Authors: |
Shou-Te Chang
|
| Pages: |
270 |
| ISBN-13: |
978-981-12-7724-5 |
| Categories: |
Books
|
| LSN: |
981-12-7724-9 |
| Barcode: |
9789811277245 |
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