**ERIC Number:**ED214767

**Record Type:**RIE

**Publication Date:**1979

**Pages:**92

**Abstractor:**N/A

**Reference Count:**0

**ISBN:**N/A

**ISSN:**N/A

Elements of the Theory of Generalized Inverses for Matrices.

Cline, Randall E.

This document is designed to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. The approach used is to: (1) develop the material in terms of full-rank factorizations and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) include an appendix of hints for exercises. In addition, the Moore-Penrose inverse of a matrix is introduced and its use in characterizing particular solutions to systems of equations is immediately explored before many of its algebraic properties are established. This is done to provide some motivation for considering generalized inverses before developing the algebraic theory. This material was originally assembled as lecture notes for senior seminars in mathematics at the University of Tennessee, and requires a knowledge of basic matrix theory as found in many current introductory texts. It is noted that it may be helpful to have a standard linear algebra textbook for reference, as fundamental definitions and concepts are used without the detailed discussion that would be included in a self-contained work. (MP)

**Publication Type:**Guides - Classroom - Learner

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**National Science Foundation, Washington, DC.

**Authoring Institution:**Education Development Center, Inc., Newton, MA.

**Identifiers:**Matrix Operations; Properties (Mathematics)

**Note:**For related documents, see SE 036 459, SE 036 466, and SE 036 468-469.