# Linear and Geometric Algebra

@inproceedings{Macdonald2011LinearAG, title={Linear and Geometric Algebra}, author={Alan Macdonald}, year={2011} }

Linear algebra is part of the standard undergraduate mathematics curriculum because it is of central importance in pure and applied mathematics. It was not always so. The wide acceptance of vector methods did not occur until early in the twentieth century. The pioneers were two physicists: the American Josiah Willard Gibbs and the Englishman Oliver Heaviside, beginning in the late 1870’s. Linear algebra allows easy algebraic manipulation of vectors. But it is not the latest word on the…

## 44 Citations

Geometry of complex data

- Computer ScienceIEEE Aerospace and Electronic Systems Magazine
- 2016

This tutorial provides a basic introduction to geometric algebra and presents formulations of known electrical engineering and signal processing concepts to illustrate some inherent advantages of geometric algebra for formulating and solving problems involving vectors.

Solution of a High-School Algebra Problem to Illustrate the Use of Elementary Geometric (Clifford) Algebra

- Mathematics
- 2018

This document is the first in what is intended to be a collection of solutions of high-school-level problems via Geometric Algebra (GA). GA is very much "overpowered" for such problems, but students…

First Steps of Vector Differential Calculus

- Computer Science
- 2020

The fundamentals of the *vector differential calculus* part of *universal geometric calculus* are treated, giving details, which are usually skipped in more advanced discussions of the subject matter, to serve as reference material.

Geometric algebra| An introduction with applications in Euclidean and conformal geometry

- Mathematics
- 2013

This thesis presents an introduction to geometric algebra for the uninitiated. It contains examples of how some of the more traditional topics of mathematics can be reexpressed in terms of geometric…

Introduction to Clifford's Geometric Algebra

- Mathematics, Computer Science
- 2013

This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model.

Geometric Algebra

- Physics, Mathematics
- 2012

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…

Via Geometric (Clifford) Algebra: Equation for Line of Intersection of Two Planes

- Mathematics
- 2019

As a high-school-level example of solving a problem via Geometric Algebra (GA), we show how to derive an equation for the line of intersection between two given planes. The solution method that we…

Calculating the Angle Between Projections of Vectors Via Geometric (Clifford) Algebra

- Mathematics
- 2018

We express a problem from visual astronomy in terms of Geometric (Clifford) Algebra, then solve the problem by deriving expressions for the sine and cosine of the angle between projections of two…

Geometric calculus on pseudo-Riemannian manifolds.

- Mathematics
- 2019

Geometric calculus provides---through methods of Clifford (geometric) algebra---useful connections between vector calculus, tensor calculus, and differential forms, and extends these to the calculus…

Geometric Algebra, Extended Cross-Product and Laplace Transform for Multidimensional Dynamical Systems

- Mathematics
- 2017

This contribution describes a new approach for solving linear system of algebraic equations and differential equations using Laplace transform by the extended-cross product. It will be shown that a…