English
资源说明：This book is meant to provide an introduction to vectors, matrices, and least
squares methods, basic topics in applied linear algebra. Our goal is to give the
beginning student, with little or no prior exposure to linear algebra, a good grounding
in the basic ideas, as well as an appreciation for how they are used in many
applications, including data tting, machine learning and articial intelligence, tomography,
navigation, image processing, nance, and automatic control systems.
The background required of the reader is familiarity with basic mathematical
notation. We use calculus in just a few places, but it does not play a critical
role and is not a strict prerequisite. Even though the book covers many topics
that are traditionally taught as part of probability and statistics, such as tting
mathematical models to data, no knowledge of or background in probability and
statistics is needed.
The book covers less mathematics than a typical text on applied linear algebra.
We use only one theoretical concept from linear algebra, linear independence, and
only one computational tool, the QR factorization; our approach to most applications
relies on only one method, least squares (or some extension). In this sense
we aim for intellectual economy: With just a few basic mathematical ideas, concepts,
and methods, we cover many applications. The mathematics we do present,
however, is complete, in that we carefully justify every mathematical statement.
In contrast to most introductory linear algebra texts, however, we describe many
applications, including some that are typically considered advanced topics, like
document classication, control, state estimation, and portfolio optimization.
The book does not require any knowledge of computer programming, and can be
used as a conventional textbook, by reading the chapters and working the exercises
that do not involve numerical computation. This approach however misses out on
one of the most compelling reasons to learn the material: You can use the ideas and
methods described in this book to do practical things like build a prediction model
from data, enhance images, or optimize an investment portfolio. The growing power
of computers, together with the development of high level computer languages
and packages that support vector and matrix computation, have made it easy to
use the methods described in this book for real applications. For this reason we
hope that every student of this book will complement their study with computer
programming exercises and projects, including some that involve real data. This
book includes some generic exercises that require computation; additional ones,
and the associated data les and language-specic resources, are available on-line.
If you read the whole book, work some of the exercises, and carry out computer
viii Preface
exercises to implement or use the ideas and methods, you will learn a lot. While
there will still be much for you to learn, you will have seen many of the basic ideas
behind modern data science and other application areas.
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