Revising this textbook has been a special challenge, for a very nice reason. So many people have read this book, and taught from it, and even loved it. The spirit of the book could never change. This text was written to help our teaching of linear algebra keep up with the enormous importance of this subject—which just continues to grow.

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Preface I wrote this book to help machine learning practitioners, like you, get on top of linear algebra, fast. Linear Algebra Is Important in Machine Learning There is no doubt that linear algebra is important in machine learning. Linear algebra is the mathematics of data. It’s all vectors and matrices of numbers. Modern statistics is described using the notation of linear algebra and modern statistical methods harness the tools of linear algebra. Modern machine learning methods are described the same way, using the notations and tools drawn directly from linear algebra. Even some classical methods used in the field, such as linear regression via linear least squares and singular-value decomposition, are linear algebra methods, and other methods, such as principal component analysis, were born from the marriage of linear algebra and statistics. To read and understand machine learning, you must be able to read and understand linear algebra. Practitioners Study Linear Algebra Too Early If you ask how to get started in machine learning, you will very likely be told to start with linear algebra. We know that knowledge of linear algebra is critically important, but it does not have to be the place to start. Learning linear algebra first, then calculus, probability, statistics, and eventually machine learning theory is a long and slow bottom-up path. A better fit for developers is to start with systematic procedures that get results, and work back to the deeper understanding of theory, using working results as a context. I call this the top-down or results-first approach to machine learning, and linear algebra is not the first step, but perhaps the second or third. Practitioners Study Too Much Linear Algebra When practitioners do circle back to study linear algebra, they learn far more of the field than is required for or relevant to machine learning. Linear algebra is a large field of study that has tendrils into engineering, physics and quantum physics. There are also

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