  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 certainly 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. Several interesting properties are derived. The main
application of these new structures in Markov chains and Leontief economic
models are also given in this chapter. The final chapter suggests 161 problems
mainly to make the reader understand this new concept and apply them.
