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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).

• 06:28, 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$$ coordinate, a...")
• 06:16, 15 July 2023 Eric Lengyel talk contribs created page File:Plane.svg
• 06:16, 15 July 2023 Eric Lengyel talk contribs uploaded File:Plane.svg
• 06:15, 15 July 2023 Eric Lengyel talk contribs created page Grade and antigrade (Created page with "The ''grade'' of a basis element in a geometric algebra is equal to the number of basis vectors present in its factorization. An arbitrary element whose components all have the same grade is also said to have that grade. The ''antigrade'' of a basis element is equal to the number of basis vectors absent from its factorization. The grade of an element $$\mathbf x$$ is denoted by $$\operatorname{gr}(\mathbf x)$$, and the antigrade is denoted by $$\operatorname{ag}(\mathb...")
• 06:14, 15 July 2023 Eric Lengyel talk contribs created page Reverses (Created page with "''Reverses'' are unary operations in geometric algebra that are analogs of conjugate or transpose operations. For any element $$\mathbf x$$ that is the wedge product of $$k$$ vectors, the ''reverse'' of $$\mathbf x$$, which we denote by $$\mathbf{\tilde x}$$, is the result of multiplying those same $$k$$ vectors in reverse order. For example, the reverse of $$\mathbf e_{234}$$ is $$\mathbf e_4 \wedge \mathbf e_3 \wedge \mathbf e_2$$, which we would write as $$-\math...")
• 06:14, 15 July 2023 Eric Lengyel talk contribs created page File:Reverses.svg
• 06:14, 15 July 2023 Eric Lengyel talk contribs uploaded File:Reverses.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs created page File:Plane line.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs uploaded File:Plane line.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs created page File:Line point.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs uploaded File:Line point.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs created page File:Plane point.svg
• 06:12, 15 July 2023 Eric Lengyel talk contribs uploaded File:Plane point.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs created page File:Line plane.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs uploaded File:Line plane.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs created page File:Point line.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs uploaded File:Point line.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs created page File:Point plane.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs uploaded File:Point plane.svg
• 06:11, 15 July 2023 Eric Lengyel talk contribs created page Projections (Created page with "Projections and antiprojections of one geometric object onto another can be accomplished using interior products as described below. The formulas on this page are general and do not require the geometric objects to be unitized. Most of them become simpler if unitization can be assumed. == Projection == The geometric projection of an object $$\mathbf x$$ onto an object $$\mathbf y$$ is given by the general formula $$(\mathbf y_\unicode{x25CB} \mathbin{\unicode{...")
• 06:10, 15 July 2023 Eric Lengyel talk contribs created page Euclidean distance (Created page with "The Euclidean distance between geometric objects can be measured by using commutators to calculate homogeneous magnitudes. The following table lists formulas for Euclidean distances between the main types of geometric objects in the 4D rigid geometric algebra $$\mathcal G_{3,0,1}$$. These formulas are general and do not require the geometric objects to be unitized. Most of them become simpler if unitization can be assumed. The points, lines, and p...")
• 06:10, 15 July 2023 Eric Lengyel talk contribs created page File:Distance line line.svg
• 06:10, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance line line.svg
• 06:10, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point plane.svg
• 06:10, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point plane.svg
• 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point line.svg
• 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point line.svg
• 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point point.svg
• 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point point.svg
• 06:06, 15 July 2023 Eric Lengyel talk contribs created page Flector (Created page with "400px|thumb|right|'''Figure 1.''' A flector represents an improper Euclidean isometry, which can always be regarded as a rotation about a line $$\boldsymbol l$$ and a reflection across a plane perpendicular to the same line. A ''flector'' is an operator that performs an improper isometry in Euclidean space. Such isometries encompass all possible combinations of an odd number of reflections, inversions, transflections, and rotorefle...")
• 06:06, 15 July 2023 Eric Lengyel talk contribs created page File:Improper isom.svg
• 06:06, 15 July 2023 Eric Lengyel talk contribs uploaded File:Improper isom.svg
• 06:04, 15 July 2023 Eric Lengyel talk contribs created page File:Complements.svg
• 06:04, 15 July 2023 Eric Lengyel talk contribs uploaded File:Complements.svg