Date of Award

1980

Publication Type

Doctoral Thesis

Degree Name

Ph.D.

Department

Mathematics and Statistics

Keywords

Mathematics.

Rights

info:eu-repo/semantics/openAccess

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Abstract

The theory of symbolic matrix derivatives is connected to the theory of differentials. It is shown that symbolic matrix derivatives are nothing but linear transformations of the representations of certain differentials. Representations of various differential rules are obtained and compared with those obtained by various authors. As illustrations, particular attention is given to the product rule. The theory of monotone operators is used to find the optimal solutions of various optimization problems in statistics. Some algebraic results which might be of interest by themselves are obtained to prove the main results. Optimal control models of regression experiments are presented to illustrate optimization problems with solutions on the boundary of the region of concern.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1980 .W654. Source: Dissertation Abstracts International, Volume: 41-03, Section: B, page: 0996. Thesis (Ph.D.)--University of Windsor (Canada), 1980.

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