Geometric Multiplication of Vectors pp 1-74 | Cite as

# Basic Concepts

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## Abstract

We denote vectors by small Latin letters in *italic* format wherever there is no possibility of confusion. If necessary, we will use the **bold** format or arrows. For *multivectors*, we use uppercase *italic* format, and for real numbers we use the Greek alphabet or Latin letters in roman format. If we define an orthonormal basis in a vector space, then the number of unit vectors that square to 1 is denoted by *p*, that square to −1 by *q*, and that square to 0 by *r*. The common designation for such a vector space is *ℜ*(*p*, *q*, *r*) or *ℜ*^{p, q, r}, while the triplet (*p*, *q*, *r*) defines the *signature*. For the *geometric algebra* of the *n*-dimensional Euclidean vector space \( {\Re}^n \) (with *q* = *r* = 0), we use the abbreviation *Cln*, motivated by the surname Clifford.

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