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Geometric Algebra by Eric Chisolm
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About this book :-
Geometric Algebra
Eric Chisolm.
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways:
1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension.
2. It defines a product that’s strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane.
Book Detail :-
Title: Geometric Algebra
Edition:
Author(s): Eric Chisolm
Publisher:
Series:
Year: 2012
Pages: 92
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Geometric Algebra
Eric Chisolm
cover the following topics.
Introduction
Motivation, Simple applications, Where now?, References and comments
Definitions and axioms
The contents of a geometric algebra
The inner, outer, and geometric products
The inner, outer, and geometric products of a vector with anything, The general inner product, outer product, and geometric product, The geometric meaning of the inner and outer products
Other operations
Grade involution, Reversion, Clifford conjugation, The scalar product, The dual, The commutator
Geometric algebra in Euclidean space
Two dimensions and complex numbers, Three dimensions, Pauli matrices, and quaternions
More on projections, reflections, and rotations
Orthogonal projections and rejections, Projecting a vector into a subspace, Projecting a multivector into a subspace, Reflections, Reflecting a vector in a subspace, Reflecting a multivector in a subspace, Rotations, Rotating a multivector in a plane, Rotations in three dimensions
Frames and bases
Reciprocal frames, Multivector bases, Orthogonal projections using frames
Linear algebra
Preliminaries, The adjoint, Normal operators, Symmetric and skew symmetric operators, Isometries and orthogonal transformations, Isometries and versors, Rotors and biversors, Extending linear functions to the whole algebra, Outermorphisms, Outermorphism extensions, Eigenblades and invariant subspaces, The determinant
Applications
Classical particle mechanics, Angular momentum as a bivector, The Kepler problem
Summary of definitions and formulas
Notation, Axioms, Contents of a geometric algebra, The inner, outer, and geometric products, The geometric meaning of the inner and outer products, Grade involution, Reversion, Clifford conjugation, The scalar product and norm, The dual, The commutator, Frames and bases, The adjoint of a linear operator, Symmetric and skew symmetric operators, Isometries and orthogonal transformations, Eigenvalues, invariant subspaces, and determinants
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