Question

Axiomatic introduction of the geometric product (Clifford Algebra)

score 331 · Answer 1 · 2026-04-13 21:02:54

331

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Axiomatic introduction of the geometric product (Clifford Algebra)

Published on 13 Apr 2026 - 21:02

score 146 · Answer 2 · 2026-04-14 07:44:36

146

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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 14 Apr 2026 - 7:44

score 120 · Answer 3 · 2026-03-26 07:58:24

120

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Geometric understanding of "Pauli vector" determinant?

Published on 26 Mar 2026 - 7:58

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

66

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

Published on 25 Mar 2026 - 11:33

score 40 · Answer 5 · 2026-03-26 07:58:56

40

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

Published on 26 Mar 2026 - 7:58

score 202 · Answer 6 · 2026-03-26 08:00:52

202

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

Published on 26 Mar 2026 - 8:00

score 81 · Answer 7 · 2026-03-26 08:00:31

81

Views

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

Published on 26 Mar 2026 - 8:00

score 105 · Answer 8 · 2026-03-26 09:42:40

105

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

Published on 26 Mar 2026 - 9:42

score 38 · Answer 9 · 2026-03-26 09:40:35

38

Views

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

Published on 26 Mar 2026 - 9:40

score 101 · Answer 10 · 2026-03-26 07:56:53

101

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extended Clifford algebra

Published on 26 Mar 2026 - 7:56

score 116 · Answer 11 · 2026-05-10 21:50:07

116

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Representing the spin group with rotors

Published on 10 May 2026 - 21:50

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 48 · Answer 13 · 2026-03-26 09:38:38

48

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

Published on 26 Mar 2026 - 9:38

score 108 · Answer 14 · 2026-04-09 19:13:42

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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