Grassmann Algebra Volume 2 Extensions

Due to circumstances beyond the author's control, this abridged draft edition of the book is being published now. Unfortunately, there will not be another edition, so you may miss some expected features such as page numbers in the table of contents, a comprehensive bibliography and references, an index, and a well-reviewed text.

Volume 2 of the book follows on from Volume 1, so it may be necessary to refer back to Volume 1 for context. This volume explores how hypercomplex and associative algebras are intricately connected to Grassmann algebra. The book reveals that quaternions, octonions, their split variants, geometric and Clifford algebras are essentially forms of Grassmann algebra. This is achieved by extending the exterior and interior product operations to define a range of products known as the generalized Grassmann product.

By utilizing the generalized Grassmann product, the book illustrates how hypercomplex, geometric, and Clifford products can be expressed as linear combinations. These combinations are constrained by scalar coefficients limited to unity or negative unity, ensuring properties like associativity. The book ultimately identifies four associative product operations, including the geometric and Clifford products, all operating within the realm of Grassmann entities.

In summary, this book showcases the construction of significant linear algebras like hypercomplex, geometric, and Clifford algebras exclusively within the framework of Grassmann algebra. It achieves this by establishing specialized product operations based on the exterior and interior products.

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