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Linear Transformations on \({\mathbb{R}}^{n}\)

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Abstract

The definition of a linear transformation on \({\mathbb{R}}^{n}\), and its natural extension to an outermorphism on all of the geometric algebra \({\mathbb{G}}_{n}\), is given. The tools of geometric algebra, such as the a-derivative and the simplicial k-derivative, are used to study its basic properties. We introduce the adjoint linear transformation and use it to derive the inverse of a nonsingular transformation.

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  1. Departamento de Física y Matemáticas, Universidad de Las Américas, Puebla, Mexico

    Garret Sobczyk

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Sobczyk, G. (2013). Linear Transformations on \({\mathbb{R}}^{n}\) . In: New Foundations in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8385-6_7

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