Question

Geometric Algebra: show $ A_r \cdot B_s = (-1)^{r(s-1)} B_s \cdot A_r$ and $A_r\wedge B_s = (-1)^{rs} B_s \wedge A_r$ from Hestenes and Sobczyk's book

score 78 · Answer 1 · 2026-02-23 09:01:49

78

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Geometric Algebra: show $ A_r \cdot B_s = (-1)^{r(s-1)} B_s \cdot A_r$ and $A_r\wedge B_s = (-1)^{rs} B_s \wedge A_r$ from Hestenes and Sobczyk's book

Published on 23 Feb 2026 - 9:01

score 17 · Answer 2 · 2026-02-27 18:14:33

17

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Reducible representations of the Clifford Algebra

Published on 27 Feb 2026 - 18:14

score 106 · Answer 3 · 2023-10-26 00:39:46

106

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Lorentz algebra problem. Relation of $\mathfrak{s}\mathfrak{o}(3,1)$, $\mathfrak{s}{u}(2)$, $\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$

Published on 26 Oct 2023 - 0:39

score 26 · Answer 4 · 2023-10-26 18:18:26

26

Views

The algebra $\Gamma^\infty(\mathbb{C}l(M))$ is generated by $\Omega^1(M)$

Published on 26 Oct 2023 - 18:18

score 71 · Answer 5 · 2026-03-25 16:01:15

71

Views

Do the Clifford Algebra products $e_1e_0$, $e_1e_{-1}$ and $e_0e_{-1}$ anticommute?

Published on 25 Mar 2026 - 16:01

score 23 · Answer 6 · 2026-03-25 11:06:31

23

Views

How does the following representation of $\mathbb{C}l(3)$ decompose into irreducibles?

Published on 25 Mar 2026 - 11:06

score 66 · Answer 7 · 2023-11-02 21:07:46

Projective Geometric Algebra - what does an "inheritance property" mean in this context and how does it relate to line representations as bivectors?

score 46 · Answer 8 · 2023-11-07 00:49:55

46

Views

On triality, $Cl_{0,6}(\mathbb{R})$, and the outer automorphism of $S_6$

Published on 07 Nov 2023 - 0:49

score 322 · Answer 9 · 2023-11-08 23:54:19

322

Views

Understanding's Wikipedia's definition of a spinor

Published on 08 Nov 2023 - 23:54

score 80 · Answer 10 · 2026-03-25 14:24:36

80

Views

Show that $\tfrac{1}{2}(b B\cdot (c \wedge a) - a B\cdot (c \wedge b)) = (c\cdot b) a \cdot B $ in geometric algebra

Published on 25 Mar 2026 - 14:24

score 37 · Answer 11 · 2026-03-25 19:06:23

37

Views

Express reflection w.r.t. combination of vectors as combinations of reflection w.r.t. vectors

Published on 25 Mar 2026 - 19:06

score 74 · Answer 12 · 2026-03-25 14:24:34

74

Views

How to derive the Log and Exp functions of a Geometric Algebra Rotor for Spherical Interpolation (Slerp) in 4D

Published on 25 Mar 2026 - 14:24

score 87 · Answer 13 · 2023-11-22 17:25:03

87

Views

Seeking 4x4 Real Matrix Representation of Generators for Clifford Algebra Cl(3,1)

Published on 22 Nov 2023 - 17:25

score 81 · Answer 14 · 2026-03-25 19:06:21

81

Views

What is a Geometric Interpretation of the Product of two Blades?

Published on 25 Mar 2026 - 19:06

score 42 · Answer 15 · 2023-11-28 04:19:55

42

Views

Seeking Correct 2x2 Matrix Representation for CL(1,1) in Clifford Algebra

Published on 28 Nov 2023 - 4:19

List Question

Geometric Algebra: show $ A_r \cdot B_s = (-1)^{r(s-1)} B_s \cdot A_r$ and $A_r\wedge B_s = (-1)^{rs} B_s \wedge A_r$ from Hestenes and Sobczyk's book

Reducible representations of the Clifford Algebra

Lorentz algebra problem. Relation of $\mathfrak{s}\mathfrak{o}(3,1)$, $\mathfrak{s}{u}(2)$, $\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$

The algebra $\Gamma^\infty(\mathbb{C}l(M))$ is generated by $\Omega^1(M)$

Do the Clifford Algebra products $e_1e_0$, $e_1e_{-1}$ and $e_0e_{-1}$ anticommute?

How does the following representation of $\mathbb{C}l(3)$ decompose into irreducibles?

Projective Geometric Algebra - what does an "inheritance property" mean in this context and how does it relate to line representations as bivectors?

On triality, $Cl_{0,6}(\mathbb{R})$, and the outer automorphism of $S_6$

Understanding's Wikipedia's definition of a spinor

Show that $\tfrac{1}{2}(b B\cdot (c \wedge a) - a B\cdot (c \wedge b)) = (c\cdot b) a \cdot B $ in geometric algebra

Express reflection w.r.t. combination of vectors as combinations of reflection w.r.t. vectors

How to derive the Log and Exp functions of a Geometric Algebra Rotor for Spherical Interpolation (Slerp) in 4D

Seeking 4x4 Real Matrix Representation of Generators for Clifford Algebra Cl(3,1)

What is a Geometric Interpretation of the Product of two Blades?

Seeking Correct 2x2 Matrix Representation for CL(1,1) in Clifford Algebra

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