In contrast to most introductory linear algebra texts, however, we describe many applications, including some that are typically considered advanced topics, like document classification, control, state estimation, and portfolio optimization. The mathematics we do present, however, is complete, in that we carefully justify every mathematical statement.
In this sense we aim for intellectual economy: With just a few basic mathematical ideas, concepts, and methods, we cover many applications. 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). The book covers less mathematics than a typical text on applied linear algebra. Even though the book covers many topics that are traditionally taught as part of probability and statistics, such as fitting mathematical models to data, no knowledge of or background in probability and statistics is needed. We use calculus in just a few places, but it does not play a critical role and is not a strict prerequisite. The background required of the reader is familiarity with basic mathematical notation.
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 fitting, machine learning and artificial intelligence, tomography, navigation, image processing, finance, and automatic control systems. This book is meant to provide an introduction to vectors, matrices, and least squares methods, basic topics in applied linear algebra.
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