Surprised by the dirth of research-level books on linear algebra, Kandasamy (mathematics, Indian Institute of Technology, India) endeavored to prepare this book, which not only studies the Smarandache analogues of linear algebra and its applications, but "also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense" (from the preface). Knowledge of linear algebra is assumed, but the first chapter introduces basic concepts and results (without proof) and also includes discussion of bilinear forms and properties, representations of finite groups and transformation of vector spaces, semivector spaces and semilinear algebra, as well as some standard applications. After coverage of Smarandache analgues of the various concepts related to linear algebra, dicussion turns to applications, including the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models, both of which topics have industrial applications. A final chapter of 131 problems is also included. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)