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 70 · Answer 2 · 2023-11-01 23:48:51

70

Views

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

Published on 01 Nov 2023 - 23:48

score 69 · Answer 3 · 2023-11-02 08:02:57

69

Views

On vector multiplication

Published on 02 Nov 2023 - 8:02

score 34 · Answer 4 · 2023-11-03 00:36:35

34

Views

Norm of a Multivector in $\wedge \mathbb{R}^3$ for calculating the arrea of a polygon.

Published on 03 Nov 2023 - 0:36

score 115 · Answer 5 · 2023-11-04 20:41:46

115

Views

Intuition for why a 90 degree rotation of a vector about an arbitrary axis can be expressed as 3 90 degree rotations of the vector's projections.

Published on 04 Nov 2023 - 20:41

score 79 · Answer 6 · 2023-11-10 22:25:57

79

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 10 Nov 2023 - 22:25

score 128 · Answer 7 · 2023-11-13 09:47:07

128

Views

Cartan's magic formula and geometric product

Published on 13 Nov 2023 - 9:47

score 86 · Answer 8 · 2023-11-15 07:46:34

86

Views

Reference: Is a simple k-vector an equivalence class?

Published on 15 Nov 2023 - 7:46

score 73 · Answer 9 · 2023-11-18 18:35:53

73

Views

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

Published on 18 Nov 2023 - 18:35

score 80 · Answer 10 · 2023-11-23 14:40:41

80

Views

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

Published on 23 Nov 2023 - 14:40

score 46 · Answer 11 · 2023-12-10 01:22:16

46

Views

Computing $x\cdot e_n \cdot x \cdot e_n$ in a Clifford algebra over $\mathbb{C}^d$

Published on 10 Dec 2023 - 1:22

score 93 · Answer 12 · 2023-12-11 16:19:09

93

Views

What is the intuition behind the regressive product and its axioms?

Published on 11 Dec 2023 - 16:19

score 44 · Answer 13 · 2023-12-16 09:17:44

44

Views

Viewing vectors in a Clifford algebra as reflections

Published on 16 Dec 2023 - 9:17

score 118 · Answer 14 · 2024-01-02 22:16:19

118

Views

Is the inverse of a $k$-vector a $k$-vector?

Published on 02 Jan 2024 - 22:16

score 73 · Answer 15 · 2024-01-06 09:07:17

73

Views

In geometric algebra, what is the grade of a k-vector in an n-dimensional space？

Published on 06 Jan 2024 - 9:07

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

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

On vector multiplication

Norm of a Multivector in $\wedge \mathbb{R}^3$ for calculating the arrea of a polygon.

Intuition for why a 90 degree rotation of a vector about an arbitrary axis can be expressed as 3 90 degree rotations of the vector's projections.

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

Cartan's magic formula and geometric product

Reference: Is a simple k-vector an equivalence class?

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

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

Computing $x\cdot e_n \cdot x \cdot e_n$ in a Clifford algebra over $\mathbb{C}^d$

What is the intuition behind the regressive product and its axioms?

Viewing vectors in a Clifford algebra as reflections

Is the inverse of a $k$-vector a $k$-vector?

In geometric algebra, what is the grade of a k-vector in an n-dimensional space？

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