MATRIX CALCULATIONS AND APPLICATIONS,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Matrix methods are an essential part of the mathematical equipment used in many areas of applied mathematics, the sciences, and engineering. The purpose of these lectures is to introduce the applied scientist to this powerful tool. Chapter I is concerned with the basic definitions and rules for manipulating matrices. The object of placing Chapter II, concerned with an engineering application, directly after Chapter I, is to emphasize that many of the applications of matrices require only the simplest properties of matrices - little more, in fact, than the definition of multiplication and the idea of the inverse matrix. The topics treated in the remaining three chapters are a small selection from a vast number of possibilities. Chapter III deals with the method of successive elimination for solving linear equations. Chapters IV and V deal with topics which are of central importance in matrix applications, namely ideas connected with the linear independence of vectors, and concepts connected with eigenvectors and eigenvalues.
- Theoretical Mathematics