These linear algebras may then be seen as extensions of the Grassmann algebra and not new algebras in their own right. Their entities are Grassmann expressions and so too are any of the specialised products of their entities.

The power of this approach is that one may work in a space of any dimension and bring to bear an extended collection of product operations onto any entities of the space.

These new product operations comprise

the generalised product

the hypercomplex product

the general associative product

the geometric product

the Clifford product

The structure of this book

The book comprises six chapters numbered from 7 to 12 to follow chapters 1 to 6 of Volume 1.

The first chapter, Chapter 7, is introductory.

Chapters 8 to 12 discuss the main purpose of the book.

The coda at the end of the book comprises various reference compilations.

The purpose of this book is to show how some important linear algebras such as the hypercomplex, geometric and Clifford algebras can be constructed entirely within Grassmann algebra by defining specialised product operations using only the exterior and interior products, but no extra axioms.