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Combined display of all available logs of Rigid Geometric Algebra. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 06:45, 15 July 2023 Eric Lengyel talk contribs created page Trivectors (Redirected page to Trivector) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Bivectors (Redirected page to Bivector) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Translations (Redirected page to Translation) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Reflections (Redirected page to Reflection) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Rotations (Redirected page to Rotation) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Planes (Redirected page to Plane) Tag: New redirect
• 06:44, 15 July 2023 Eric Lengyel talk contribs created page Lines (Redirected page to Line) Tag: New redirect
• 06:43, 15 July 2023 Eric Lengyel talk contribs created page Points (Redirected page to Point) Tag: New redirect
• 06:43, 15 July 2023 Eric Lengyel talk contribs created page Trivector (Created page with "A ''trivector'' in a geometric algebra is an element composed entirely of components having grade 3. == See Also == * Vector * Bivector * Antivector")
• 06:42, 15 July 2023 Eric Lengyel talk contribs created page Bivector (Created page with "A ''bivector'' in a geometric algebra is an element composed entirely of components having grade 2. == See Also == * Vector * Trivector * Antivector")
• 06:42, 15 July 2023 Eric Lengyel talk contribs created page Antivector (Created page with "An ''antivector'' in a geometric algebra is an element composed entirely of components having antigrade 1. In an ''n''-dimensional geometric algebra, these are the elements having grade $$n - 1$$. == See Also == * Vector * Bivector * Trivector")
• 06:41, 15 July 2023 Eric Lengyel talk contribs created page Antivectors (Redirected page to Antivector) Tag: New redirect
• 06:40, 15 July 2023 Eric Lengyel talk contribs created page Vector (Created page with "A ''vector'' in a geometric algebra is an element composed entirely of components having grade 1. == See Also == * Bivector * Trivector * Antivector")
• 06:40, 15 July 2023 Eric Lengyel talk contribs created page Vectors (Redirected page to Vector) Tag: New redirect
• 06:39, 15 July 2023 Eric Lengyel talk contribs created page Antiscalars (Redirected page to Scalars and antiscalars) Tag: New redirect
• 06:39, 15 July 2023 Eric Lengyel talk contribs created page Scalars (Redirected page to Scalars and antiscalars) Tag: New redirect
• 06:37, 15 July 2023 Eric Lengyel talk contribs created page Antigrade (Redirected page to Grade and antigrade) Tag: New redirect
• 06:36, 15 July 2023 Eric Lengyel talk contribs created page Grade (Redirected page to Grade and antigrade) Tag: New redirect
• 06:36, 15 July 2023 Eric Lengyel talk contribs created page Commutators (Created page with "In geometric algebra, there are four ''commutator'' products defined as follows. :$$[\mathbf a, \mathbf b]^{\Large\unicode{x27D1}}_- = \dfrac{1}{2}\left(\mathbf a \mathbin{\unicode{x27D1}} \mathbf b - \mathbf b \mathbin{\unicode{x27D1}} \mathbf a\right)$$ :$$[\mathbf a, \mathbf b]^{\Large\unicode{x27D1}}_+ = \dfrac{1}{2}\left(\mathbf a \mathbin{\unicode{x27D1}} \mathbf b + \mathbf b \mathbin{\unicode{x27D1}} \mathbf a\right)$$ :$$[\mathbf a, \mathbf b]^{\Large\unicode...")
• 06:35, 15 July 2023 Eric Lengyel talk contribs created page Point (Created page with "400px|thumb|right|'''Figure 1.''' A point is the intersection of a 4D vector with the 3D subspace where $$w = 1$$. In the 4D rigid geometric algebra $$\mathcal G_{3,0,1}$$, a ''point'' $$\mathbf p$$ is a vector having the general form :$$\mathbf p = p_x \mathbf e_1 + p_y \mathbf e_2 + p_z \mathbf e_3 + p_w \mathbf e_4$$ . All points possess the geometric property. The bulk of a point is given by its $$x$$, $$y$$, and $$z$$ coordinates, and...")
• 06:35, 15 July 2023 Eric Lengyel talk contribs created page File:Point.svg
• 06:35, 15 July 2023 Eric Lengyel talk contribs uploaded File:Point.svg
• 06:33, 15 July 2023 Eric Lengyel talk contribs created page Duality (Created page with "480px|thumb|right|'''Figure 1.''' The coordinates $$(p_x, p_y, p_z, p_w)$$ can be interpreted as the one-dimensional span of a single vector representing a homogeneous point or as the $$(n - 1)$$-dimensional span of all orthogonal vectors representing a homogeneous plane. Geometrically, these two interpretations are dual to each other, and their distances to the origin are reciprocals of each other. The concept of duality can be understood geometric...")
• 06:33, 15 July 2023 Eric Lengyel talk contribs created page File:Duality.svg
• 06:33, 15 July 2023 Eric Lengyel talk contribs uploaded File:Duality.svg
• 06:30, 15 July 2023 Eric Lengyel talk contribs created page Wedge products (Redirected page to Exterior products) Tag: New redirect
• 06:29, 15 July 2023 Eric Lengyel talk contribs created page Geometric products (Created page with "The ''geometric product'' is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct. == Geometric Product == The geometric product between two elements $$\mathbf a$$ and $$\mathbf b$$ has often been written by simply juxtaposing its operands as $$\mathbf{ab}$$ without the use of any infix operator. However, this clearly becomes impractical when both a product and antiproduct...")
• 06:29, 15 July 2023 Eric Lengyel talk contribs created page File:GeometricAntiproduct.svg
• 06:29, 15 July 2023 Eric Lengyel talk contribs uploaded File:GeometricAntiproduct.svg
• 06:29, 15 July 2023 Eric Lengyel talk contribs created page File:GeometricProduct.svg
• 06:29, 15 July 2023 Eric Lengyel talk contribs uploaded File:GeometricProduct.svg
• 06:28, 15 July 2023 Eric Lengyel talk contribs created page Exterior products (Created page with "The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the geometric product in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct. The exterior product between two elements $$\mathbf a$$ and $$\mathbf b$$ generally combines their spatial extents, and the magnitude of the result indicates how close they are to being orthogonal. If the spatial extents of $$\m...")
• 06:28, 15 July 2023 Eric Lengyel talk contribs created page File:AntiwedgeProduct.svg
• 06:28, 15 July 2023 Eric Lengyel talk contribs uploaded File:AntiwedgeProduct.svg
• 06:28, 15 July 2023 Eric Lengyel talk contribs created page File:WedgeProduct.svg
• 06:28, 15 July 2023 Eric Lengyel talk contribs uploaded File:WedgeProduct.svg
• 06:27, 15 July 2023 Eric Lengyel talk contribs created page Interior products (Created page with "The left and right ''interior products'' are special products in geometric algebra that are useful for performing projections. These products cancel common factors in their operands and thus reduce grade. Depending on the choice of dualization function, there are several possible interior products. We define the interior products in terms of the left and right complements. Interior products are also known as contraction products. == Left and Right Interior Prod...")
• 06:27, 15 July 2023 Eric Lengyel talk contribs created page File:InteriorAntiproduct.svg
• 06:27, 15 July 2023 Eric Lengyel talk contribs uploaded File:InteriorAntiproduct.svg
• 06:27, 15 July 2023 Eric Lengyel talk contribs created page File:InteriorProduct.svg
• 06:27, 15 July 2023 Eric Lengyel talk contribs uploaded File:InteriorProduct.svg
• 06:26, 15 July 2023 Eric Lengyel talk contribs created page Dot products (Created page with "The ''dot product'' is the inner product in geometric algebra, and it makes up the scalar part of the geometric product. There are two products with symmetric properties called the dot product and antidot product. The dot product and antidot product are important for the calculation of norms. == Dot Product == The dot product between two elements $$\mathbf a$$ and $$\mathbf b$$ is written $$\mathbf a \mathbin{\unicode{x25CF}} \mathbf b$$ and r...")
• 06:26, 15 July 2023 Eric Lengyel talk contribs created page File:AntidotProduct.svg
• 06:26, 15 July 2023 Eric Lengyel talk contribs uploaded File:AntidotProduct.svg
• 06:26, 15 July 2023 Eric Lengyel talk contribs created page File:DotProduct.svg
• 06:26, 15 July 2023 Eric Lengyel talk contribs uploaded File:DotProduct.svg
• 06:24, 15 July 2023 Eric Lengyel talk contribs created page Quaternions (Redirected page to Quaternion) Tag: New redirect
• 06:23, 15 July 2023 Eric Lengyel talk contribs created page Quaternion (Created page with "__NOTOC__ A ''quaternion'' is an operator that performs a rotation about the origin in 3D space. Conventionally, a quaternion $$\mathbf q$$ is written as :$$\mathbf q = q_w + q_x \mathbf i + q_y \mathbf j + q_z \mathbf k$$ , where the "imaginary" units $$\mathbf i$$, $$\mathbf j$$, and $$\mathbf k$$ all square to $$-1$$ and multiply according to the rules :$$\mathbf{ij} = -\mathbf{ji} = \mathbf k$$ :$$\mathbf{jk} = -\mathbf{kj} = \mathbf i$$ :$$\mathbf{ki} = -\mathbf{...")
• 06:20, 15 July 2023 Eric Lengyel talk contribs created page Scalars and antiscalars (Created page with "A ''scalar'' in a geometric algebra is an element having grade 0. Scalars are just ordinary real numbers, and they do not involve any basis vectors. The basis element representing the unit scalar is denoted by $$\mathbf 1$$, a boldface number one. The unit scalar $$\mathbf 1$$ is the multiplicative identity of the geometric product. For a general element $$\mathbf a$$, the notation $$a_{\mathbf 1}$$ means the scalar component of $$\mathbf a$$. An ''antiscalar'...")
• 06:16, 15 July 2023 Eric Lengyel talk contribs created page Plane (Created page with "400px|thumb|right|'''Figure 1.''' A plane is the intersection of a 4D trivector with the 3D subspace where $$w = 1$$. In the 4D rigid geometric algebra $$\mathcal G_{3,0,1}$$, a ''plane'' $$\mathbf g$$ is a trivector having the general form :$$\mathbf g = g_x \mathbf e_{423} + g_y \mathbf e_{431} + g_z \mathbf e_{412} + g_w \mathbf e_{321}$$ . All planes possess the geometric property. The bulk of a plane is given by its $$w$$ coordinate, a...")