## Mathematics and Statistics Faculty and Staff Publications

#### Title

#### Document Type

Book

#### Publication Date

2008

#### Abstract

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized world. Some other structures ought to replace linear algebras which are over a century old. Super linear algebras that use super matrices can store data not only in a block but in multiple blocks so it is certainty more powerful than the usual matrices. This book has 3 chapters. Chapter one introduces the notion of super vector spaces and enumerates a number of properties. Chapter two defines the notion of super linear algebra, super inner product spaces and super bilinear forms.

#### Publisher

InfoLearnQuest, Ann Arbor

#### ISSN

978-1-59973-065-3

#### Language (ISO)

English

#### Keywords

super linear algebra, super vector space

#### Recommended Citation

Smarandache, Florentin and W.B. Vasantha Kandasamy. "SUPER LINEAR ALGEBRA." (2008). https://digitalrepository.unm.edu/math_fsp/202

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Dynamical Systems Commons, Harmonic Analysis and Representation Commons, Other Mathematics Commons, Set Theory Commons