This book explores the Lipschitz spinorial groups (versor, pinor,
spinor and rotor groups) of a real non-degenerate orthogonal
geometry (or orthogonal geometry, for short) and how they relate to
the group of isometries of that geometry. After a concise
mathematical introduction, it offers an axiomatic presentation of
the geometric algebra of an orthogonal geometry. Once it has
established the language of geometric algebra (linear grading of
the algebra; geometric, exterior and interior products;
involutions), it defines the spinorial groups, demonstrates their
relation to the isometry groups, and illustrates their suppleness
(geometric covariance) with a variety of examples. Lastly, the book
provides pointers to major applications, an extensive bibliography
and an alphabetic index. Combining the characteristics of a
self-contained research monograph and a state-of-the-art survey,
this book is a valuable foundation reference resource on
applications for both undergraduate and graduate students.
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