Question

Axiomatic introduction of the geometric product (Clifford Algebra)

score 328 · Answer 1 · 2017-04-03 11:57:00

328

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Axiomatic introduction of the geometric product (Clifford Algebra)

Published on 03 Apr 2017 - 11:57

score 143 · Answer 2 · 2023-01-31 03:36:18

143

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In a Clifford algebra over an $n$-dimensional non-degenerate space, is a product of any number of vectors a product of at most $n$ vectors?

Published on 31 Jan 2023 - 3:36

score 119 · Answer 3 · 2023-01-31 20:09:39

119

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Geometric understanding of "Pauli vector" determinant?

Published on 31 Jan 2023 - 20:09

score 66 · Answer 4 · 2026-03-25 11:33:44

66

Views

In Geometric Algebra, does $A\tilde A=0$ imply $\tilde AA=0$?

Published on 25 Mar 2026 - 11:33

score 39 · Answer 5 · 2023-02-09 16:39:16

39

Views

Why does squaring the pseudoscalar of Clifford algebra $Cl_{2, 0}(\mathbb{R})$ equal 1?

Published on 09 Feb 2023 - 16:39

score 201 · Answer 6 · 2023-02-13 01:51:35

201

Views

Can Lawson's proof (that the canonical inclusion into a Clifford algebra is injective) be fixed?

Published on 13 Feb 2023 - 1:51

score 80 · Answer 7 · 2023-02-13 14:57:34

80

Views

Proof that a blade has no scalar part from Eric Chisolm's set of axioms for geometric algebra

Published on 13 Feb 2023 - 14:57

score 104 · Answer 8 · 2023-02-13 17:02:41

104

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How could an orthogonal transformation map an orthonormal basis to a non-orthogonal one?

Published on 13 Feb 2023 - 17:02

score 37 · Answer 9 · 2023-02-13 18:58:33

37

Views

This reduction maps to which group? General linear group reduced to spin group then squared.

Published on 13 Feb 2023 - 18:58

score 100 · Answer 10 · 2023-02-13 22:17:34

100

Views

extended Clifford algebra

Published on 13 Feb 2023 - 22:17

score 114 · Answer 11 · 2023-02-17 14:19:09

114

Views

Representing the spin group with rotors

Published on 17 Feb 2023 - 14:19

score 47 · Answer 12 · 2026-03-25 11:32:35

47

Views

How do you prove this determinant-related identity in geometric algebra?

Published on 25 Mar 2026 - 11:32

score 47 · Answer 13 · 2023-02-24 13:55:58

47

Views

Explicit isomorphism between $\mathbb{R}^+ \times {\rm Spin}^c(3,1)$ and ${\rm GL}(2,\mathbb{C})$?

Published on 24 Feb 2023 - 13:55

score 105 · Answer 14 · 2023-02-26 19:11:06

Motivation behind the definition of the outer product in geometric algebra in terms of sums of geometric products

score 115 · Answer 15 · 2026-03-25 09:53:50

115

Views

Can Fast Fourier Transform (FFT) be implemented using Clifford Algebra over GF(3)?

Published on 25 Mar 2026 - 9:53

List Question

Axiomatic introduction of the geometric product (Clifford Algebra)

In a Clifford algebra over an $n$-dimensional non-degenerate space, is a product of any number of vectors a product of at most $n$ vectors?

Geometric understanding of "Pauli vector" determinant?

In Geometric Algebra, does $A\tilde A=0$ imply $\tilde AA=0$?

Why does squaring the pseudoscalar of Clifford algebra $Cl_{2, 0}(\mathbb{R})$ equal 1?

Can Lawson's proof (that the canonical inclusion into a Clifford algebra is injective) be fixed?

Proof that a blade has no scalar part from Eric Chisolm's set of axioms for geometric algebra

How could an orthogonal transformation map an orthonormal basis to a non-orthogonal one?

This reduction maps to which group? General linear group reduced to spin group then squared.

extended Clifford algebra

Representing the spin group with rotors

How do you prove this determinant-related identity in geometric algebra?

Explicit isomorphism between $\mathbb{R}^+ \times {\rm Spin}^c(3,1)$ and ${\rm GL}(2,\mathbb{C})$?

Motivation behind the definition of the outer product in geometric algebra in terms of sums of geometric products

Can Fast Fourier Transform (FFT) be implemented using Clifford Algebra over GF(3)?

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