Emil Artin wrote a book on Geometric Algebra. Is this the same as the geometric algebra of David Hestenes?Please correct me if I'm wrong on this, I think David Hestenes geometric algebra is just clifford algebra. Did David change anything from Clifford' original geometric algebra or is he just trying to make it more well known; it seems to be very useful. Anyway, I am just curious if the textbook Geometric Algebra by Artin is also just clifford algebra or geometric algebra? I don't really know the difference between the two. Thank you.
2026-03-26 13:01:12.1774530072
What is the difference between Emil Artin's Geometric Algebra and David Hestenes Geometric Algebra?
594 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in CLIFFORD-ALGEBRAS
- What is the Clifford/geometric product in terms of the inner and exterior product
- A confusing formula in Clifford algebra
- Clifford product of force and distance
- Clifford algebra complex representation
- Minkowski metric. Scalar or tensor?
- For two unit non-oriented bivectors $A,B\in \mathbb{R}P^2\subset \Lambda^2\mathbb{R}^3$ is the mapping $\phi:(A,B)\rightarrow AB$ bijective?
- Gamma matrices and special relativity
- Spinor chiral transformation by $\psi \to \gamma^5 \psi$
- Geometric Calculus, Clifford Algebra, and Calculus of Variations
- "Square root" of a decomposition of a homogeneous polynomial to harmonic and $x^2 q$.
Related Questions in GEOMETRIC-ALGEBRAS
- A new type of curvature multivector for surfaces?
- Conditions for a C*-algebra to be Abelian
- A confusing formula in Clifford algebra
- Reverse operation on Quaternions
- What is exponential of a blade?
- For two unit non-oriented bivectors $A,B\in \mathbb{R}P^2\subset \Lambda^2\mathbb{R}^3$ is the mapping $\phi:(A,B)\rightarrow AB$ bijective?
- Geometric Calculus, Clifford Algebra, and Calculus of Variations
- Householder reflection in geometric algebra is not working for me
- How to decompose a bivector into a sum of _orthogonal_ blades?
- The Fundamental Theorem of Geometric Calculus in a lorentzian manifold
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
No, Artin's Geometric Algebra is not about what David Hesetenes is talking about.
Artin's book is a much more general course on the connection between algebra and geometry via groups. It does have a section on Clifford algebras, of which "Hestenes geometric algebras" are a special case.
So far, I've gotten a lot more use out of my copy of Artin's Geometric Algebra than out of any of the "Hestenes geometric algebra" material I've read.
I think Hestenes' principal effect has been to raise the profile of using Clifford algebras practically. I don't think I've ever seen anything about truly new results coming out of the program, but indeed since he raised the profile I think people have been taking a closer look at the Hestenes school perspective.
At one of the spectrum, I have seen some things to the effect that phrasing things with geometric algebra can make some things clearer or more memorable.
On the other end of the spectrum, I have seen people say that geometric algebra and the associated geometric calculus is just "for people uncomfortable with basic manifold theory." The whole situation reminds me a little bit of the quaternion/vector-algebra war.
Just remember not to get caught up in hype, because there is a bit of that. Personally, I someday plan to sit down and weigh these things on their virtues, but for now I'm still brushing up my manifold theory :)