Linear algebra. Textbook, exercises and applications (Q2781473)

This linear algebra textbook is totally different from the ones that one meets so abundantly. It addresses engineering students requiring a rigorous training in linear algebra, comprising mastery of the theory and aptitude in proving and calculating. The book consists of four distinct parts. NEWLINENEWLINENEWLINEThe first part comprises a memory-aid and consists of ten chapters giving the main concepts, their properties, related theorems and formulae contained in a first course on linear algebra for engineers. Proofs are not included but precise references are given to the following two books: Algèbre linéaire, by \textit{R. Cairoli}, Presses polytech. et univ. romandes (1991; Zbl 0844.15003), and Linear Algebra (Applications Version), by \textit{H. Anton} and \textit{C. Rorrès}, Wiley (1994). Each chapter ends with a set of exercises, both theoretical and numerical, for most of which the solutions are given at the end of the book.NEWLINENEWLINENEWLINEThe second part treats five different applications of linear algebra to specific engineering problems. These are: (1) the use of affine transformations in ``infography'' (the algorithmic representation of figures in a coordinate system), here of fractal objects, (2) conventional cryptography, (3) error-correcting codes, (4) Markov chains, (5) stereograms, i.e. the construction of ``magic eye'' pictures. Each of these chapters also ends with a set of exercises, with solutions provided for most of them.NEWLINENEWLINENEWLINEThe third part comprises a set of revision exercises suitable for preparing the student for examinations. As opposed to the earlier exercises in the book, these make use of material from diverse chapters. Once again, solutions for most of them are given.NEWLINENEWLINENEWLINEThe above-mentioned solutions to the exercises form the fourth part of the book.NEWLINENEWLINENEWLINEThe main objectives of this textbook are to impart a good mastery of the theory and practice of linear algebra. The applications in the second part were chosen with a view to motivating and arousing the interest of the student, in that they are topics which he will certainly have heard of before beginning his studies at university. In this sense the book is indeed novel and an interesting and useful addition to the vast array of linear algebra textbooks.