Page 13 - Linear Algebra Done Right

Preface to the Student

You are probably about to begin your second exposure to linear al-
gebra. Unlike your first brush with the subject, which probably empha-
sized Euclidean spaces and matrices, we will focus on abstract vector
spaces and linear maps. These terms will be defined later, so don’t
worry if you don’t know what they mean. This book starts from the be-
ginning of the subject, assuming no knowledge of linear algebra. The
key point is that you are about to immerse yourself in serious math-
ematics, with an emphasis on your attaining a deep understanding of
the definitions, theorems, and proofs.
You cannot expect to read mathematics the way you read a novel. If
you zip through a page in less than an hour, you are probably going too
fast. When you encounter the phrase “as you should verify”, you should
indeed do the verification, which will usually require some writing on
your part. When steps are left out, you need to supply the missing
pieces. You should ponder and internalize each definition. For each
theorem, you should seek examples to show why each hypothesis is
necessary.
Please check my web site for a list of errata (which I hope will be
empty or almost empty) and other information about this book.
I would greatly appreciate hearing about any errors in this book,
even minor ones. I welcome your suggestions for improvements, even
tiny ones.
Have fun!

Sheldon Axler
Mathematics Department
San Francisco State University
San Francisco, CA 94132, USA
e-mail: axler@math.sfsu.edu
www home page: http://math.sfsu.edu/axler

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