Welcome to the beginning of this book - an algebra book that shows
and explains further topics than those that are covered in a
primary course on linear algebra. Such course usually leaves the
student with the question "Why in the world do I have to go through
linear algebra?" which is absolutely understandable. Algebra, and
other sciences in general, are not entities that one just needs to
pass as a course. Sciences are masters that stay with you and are
always there whenever you need them, that in some occasions we do
not understand that those masters are something else. Before
talking about the importance of algebra, let us first clear some
details about this text. This book does not only contain a set of
complicated equations with heavy definitions about abstract
entities and problems that arise in several fields of mathematics,
which in many other texts, makes you feel like you're reading
Mandarin. This book also contains clear and deductive explanations
from different perspectives about those set of complicated
equations, with the hope of making them accessible and easy to
assimilate for the reader. Algebra is the science of representing
life through equations while keeping it simple. The reason for
writing this book was, at first, the decision to spread knowledge
of such a great science that is usually feared by many young
students and ignored by others, when in reality Algebra is a body
of knowledge so beautiful within itself, as well as necessary
dealing with or approaching many mathematical situations. As this
book is being developed, another reason to continue to write it
arose - there is a lack of easy-to-understand texts, which are
supposed to be the high end books that today's generation are
obligated to read, in order to understand the subjects they should
know to continue their formation in their respective careers. This
book is dedicated to those who really want to learn linear algebra.
But be warned, the journey is not promised to be easy as it will
require dedication, honesty and time from the reader; but the
journey will also be nurturing and revealing in the sense that at
the end of each chapter, the reader will be able to say "I've got
it!" in much the same way when Archimedes said "Eureka!" which
means "I've found it!" In addition, this book also contains
techniques and algorithms, along with their derivations and
examples, which are used in the real world, thus helping the reader
become a well prepared professional. Many texts, articles and
lessons were used as resources for this book, however, the most
used resource in the development of this text was common sense. You
see, mathematics is a free science, a body of knowledge that anyone
can derive on its own. This book is just a compendium of the works
of many mathematicians through the centuries, making it possible
for humankind to get to where it is today. And as life goes on, it
is probable that further developments, researches and advances will
continue. That was one of the main ideas in the background while
writing this text - to make the reader able to fully understand as
much knowledge in linear algebra as possible, especially those
concerning methods and algorithms that arose in the twentieth
century. Just as a brief comment, the first chapter of this book is
dedicated to making certain topics clear to avoid confusion, and
answering questions that usually arise during the first course in
linear algebra. The rest of the chapters are more advanced and
developed.
General
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