Introduction to Linear Algebra, by I. Farkas and M. Farkas, Adam Hilger, London, 1975, pp. 205, price $8.00. This book is said to be aimed at first-year students majoring in Mathematics, Science or Engineering, who have no background beyond their high-school knowledge. The majority of such students would find the book hard-going, even though the authors attempt to bridge the gap between the concrete structures and the axiomatic treatment of the subject. A well-motivated student could work his way through the book gaining much from the examples at the end of each chapter. He would find very little in the theory or the examples to suggest the possible applications of linear algebra. A number of misprints suggest that the book, printed in Hungary, has not been proof-read with care, and these may annoy the reader when he remembers the high price of the book. The use of the term “quadratic matrix” for a square matrix may seem strange to English-speaking readers. The contents of the book are well described by the six chapter headings: Elementary Vector Algebra, Complex Algebra, Matrix Algebra, Systems of Linear Equations, The Linear and the Euclidean Space, Linear Operators. Modern notations are used in the book, which contains answers and hints to the exercises. D. W.
Basic Matrices, An Introduction to Matrix Theory and Practice, by C. G. Broyden, Macmillan Press, London, 1975, pp. xii + 211, price s3.95, paperback, f8.95, board. This book can be recommended for anyone interested in the formulation and solution of problems in terms of matrices. Previous knowledge of matrix algebra is not necessary. The approach is novel and the pace is brisk. Most of the concepts and ideas are motivated by well-chosen paragraphs_ The consequences of each new idea are worked out before another idea is introduced. The methods discussed are chosen with computer use in mind, determinants being relegated to an appendix. It is unusual to find in a book at this level an adequate discussion of the limitations of numerical procedures. The author has provided warning signs in the right places. As a modem application of matrix theory, the Linear Programming Problem is treated in the last two of the ten chapters of the book. Answers or hints for the Exercises at the end of each chapter arid an appendix on the notation employed would have enhanced the value of this delightful little book.