Linear Transformations on $${\mathbb{R}}^{n}$$

Garret Sobczyk
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Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 7 in New Foundations in Mathematics, 2013, pp 107-116 from Springer

Abstract: 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.

Keywords: Adjoint Linear Transformation; Outermorphism; Geometric Algebra; Nonsingular Transformation; Algebraic Cofactor (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8385-6_7

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