Multidimensional Analysis: Algebras and Systems for Science and Engineering Book

Providing a generalization of "dimensional analysis," this book deals with the general mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications. Intended for a broad audience of physicists, engineers, and applied mathematicians who use linear algebra in applications involving physical measurements, the book requires only an undergraduate background in linear algebra. Applications are emphasized throughout, and a large number of examples and problems make the book suitable for classroom use as well as self-study.Read More