Introduction to Clifford's Geometric Algebra
accepted for SICE Journal of Control, Measurement, and System Integration, April 2012, (2012).
Geometric algebra was initiated byW.K. Clifford over 130 years ago.
It unifies all branches of physics, and has
found rich applications in robotics, signal processing, ray tracing,
virtual reality, computer vision, vector field processing,
tracking, geographic information systems and neural computing. This
tutorial explains the basics of geometric algebra,
with concrete examples of the plane, of 3D space, of spacetime, and
the popular conformal model. Geometric algebras are
ideal to represent geometric transformations in the general framework
of Clifford groups (also called versor or Lipschitz
groups). Geometric (algebra based) calculus allows e.g. to optimize
learning algorithms of Clifford neurons, etc.
Keywords: Hypercomplex algebra, hypercomplex analysis, geometry, science, engineering.
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