\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015c.00759}
\itemau{Andreescu, Titu}
\itemti{Essential linear algebra with applications. A problem-solving approach.}
\itemso{New York, NY: Birkh\"auser/Springer (ISBN 978-0-8176-4360-7/hbk; 978-0-8176-4636-3/ebook). x, 491~p. (2014).}
\itemab
It is well known that there are several linear algebra texbooks old and new. The richness of the subject as well as its diverse applications motivates authors to present books at various levels. The present book is a wellcomed addition at the present literature. The approach is elementray, however still rigorous and detailed. It covers the standard topics on linear algebra taught in a two-semester course, from elementray matrix theory to canonical forms and bilinear forms. The reading goes smoothly, however the audience should be mathematics, physics or engineering majors. There are well chosen examples and suggested problems integrated to the theory presented (the subtitle of the book is `A problem-solving approach'). The exersices are well chosen and most of them can be worked out by the reader. The description of the chapters of the book are as follows: 1. Matrix algebra, 2. Square matrices of order 2 (this is an interesting and useful chapter), 3. Matrices and linear equations, 4. Vector spaces and subspaces, 5. Linear transformations, 6. Duality, 7. Determinants, 8. Polynomial expressions of linear transformations and matrices, 9. Diagonalizability (including Jordan canonical form), 10. Forms (bilinear, quadratic, etc), 11. Appendix: Algebraic preliminaries. There is no glossary! The authors should try to make one and put it in some web page. In conclusion, I would be happy to teach linear algebra from this book and ask students to work on problems from it.
\itemrv{A. Arvanitoyeorgos (Patras)}
\itemcc{H65}
\itemut{linear algebra; textbook; canonical form; bilinear form; matrix algebra; linear equation; vector space; linear transformation; duality; determinant}
\itemli{doi:10.1007/978-0-8176-4636-3}
\end