E.M.S. Hitzer

*Mem. Fac. Eng. Fukui Univ.* **49**(2), (2001)

**Abstract:**
This paper briefly reviews the conventional method of obtaining the
canonical form of an antisymmetric (skewsymmetric, alternating) matrix.
Conventionally a vector space over the complex field has to be introduced.
After a short introduction to the universal mathematical "language"
Geometric Calculus, its fundamentals, i.e. its "grammar" Geometric
Algebra (Clifford Algebra) is explained. This lays the groundwork
for its real geometric and coordinate free application in order to
obtain the canonical form of an antisymmetric matrix in terms of a
bivector, which is isomorphic to the conventional canonical form.
Then concrete applications to two, three and four dimensional
antisymmetric square matrices follow. Because of the physical
importance of the Minkowski metric, the canonical form of an
antisymmetric matrix with respect to the Minkowski metric is derived
as well. A final application to electromagnetic fields concludes the work.

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