This book is called a ‘Guide to Geometric Algebra in Practice’. It is composed
of chapters by experts in the field and was conceived during the AGACSE-2010
conference in Amsterdam. As you scan the contents, you will find that all chapters
indeed use geometric algebra but that the term ‘practice’ means different things
to different authors. As we discuss the various Parts below, we guide you through
them. We will then see that appearances may deceive: some of the more theoretical
looking chapters provide useful and practical techniques.
Many people have given help and support over the last three years and I am grateful to
them all I owe a great debt to my supervisor Nick Manton for allowing me the freedom
to pursue my own interests and to my two principle collaborators Anthony Lasenby and
Stephen Gull whose ideas and inspiration were essential in shaping my research I also
thank David Hestenes for his encouragement and his company on an arduous journey to
Here we collect all tables of contents of all the books on mathematics I have written so far for the publisher.
In the rst list the topics are grouped according to their headlines, so the reader quickly can get an idea of
where to search for a given topic.In order not to make the titles too long I have in the numbering added
a for a compendium
b for practical solution procedures (standard methods etc.)
c for examples.
This book grew out of courses which I taught at Cornell University and
the University of Warwick during 1969 and 1970. I wrote it because of a
strong belief that there should be readily available a semi-historical and geometrically
motivated exposition of J. H. C. Whitehead's beautiful theory of
simple-homotopy types; that the best way to understand this theory is to
know how and why it was built.
The purpose of this section is to get a geometric understanding of linear estimation
. First. we outline how projections are computed in linear algebra
for finite dimensional vectors . Functional analysis generalizes this procedure
to some infinite-dimensional spaces (so-called Hilbert spaces). and finally. we
point out that linear estimation is a special case of an infinite-dimensional
This book is an elaboration of ideas of Irving Kaplansky introduced
in his book Rings of operators (, ).
The subject of Baer *-rings has its roots in von Neumann's theory
of 'rings of operators' (now called von Neumann algebras), that is,
*-algebras of operators on a Hilbert space, containing the identity operator,
that are closed in the weak operator topology (hence also the name
Chapter G Convexity
One major reason why linear spaces are so important for geometric analysis is that they allow us to deﬁne the notion of “line segment” in algebraic terms. Among other things, this enables one to formulate, purely algebraically, the notion of “convex set” which ﬁgures majorly in a variety of branches of higher mathematics.