Page 14 - Linear Algebra Done Right

Acknowledgments

I owe a huge intellectual debt to the many mathematicians who cre-
ated linear algebra during the last two centuries. In writing this book I
tried to think about the best way to present linear algebra and to prove
its theorems, without regard to the standard methods and proofs used
in most textbooks. Thus I did not consult other books while writing
this one, though the memory of many books I had studied in the past
surely influenced me. Most of the results in this book belong to the
common heritage of mathematics. A special case of a theorem may
first have been proved in antiquity (which for linear algebra means the
nineteenth century), then slowly sharpened and improved over decades
by many mathematicians. Bestowing proper credit on all the contrib-
utors would be a difficult task that I have not undertaken. In no case
should the reader assume that any theorem presented here represents
my original contribution.
Many people helped make this a better book. For useful sugges-
tions and corrections, I am grateful to William Arveson (for suggesting
the proof of 5.13), Marilyn Brouwer, William Brown, Robert Burckel,
Paul Cohn, James Dudziak, David Feldman (for suggesting the proof of
8.40), Pamela Gorkin, Aram Harrow, Pan Fong Ho, Dan Kalman, Robert
Kantrowitz, Ramana Kappagantu, Mizan Khan, Mikael Lindstr¨ om, Ja-
cob Plotkin, Elena Poletaeva, Mihaela Poplicher, Richard Potter, Wade
Ramey, Marian Robbins, Jonathan Rosenberg, Joan Stamm, Thomas
Starbird, Jay Valanju, and Thomas von Foerster.
Finally, I thank Springer for providing me with help when I needed
it and for allowing me the freedom to make the final decisions about
the content and appearance of this book.

xv