Functions and mappings | Linear operators | Projective geometry | Linear algebra
In linear algebra, particularly projective geometry, a semilinear map between vector spaces V and W over a field K is a function that is a linear map "up to a twist", hence semi-linear, where "twist" means "field automorphism of K". Explicitly, it is a function T : V → W that is: * additive with respect to vector addition: * there exists a field automorphism θ of K such that , where is the image of the scalar under the automorphism. If such an automorphism exists and T is nonzero, it is unique, and T is called θ-semilinear. Where the domain and codomain are the same space (i.e. T : V → V), it may be termed a semilinear transformation. The invertible semilinear transforms of a given vector space V (for all choices of field automorphism) form a group, called the general semilinear group and denoted by analogy with and extending the general linear group. The special case where the field is the complex numbers ℂ and the automorphism is complex conjugation, a semilinear map is called an antilinear map. Similar notation (replacing Latin characters with Greek) are used for semilinear analogs of more restricted linear transform; formally, the semidirect product of a linear group with the Galois group of field automorphism. For example, PΣU is used for the semilinear analogs of the projective special unitary group PSU. Note however, that it is only recently noticed that these generalized semilinear groups are not well-defined, as pointed out in – isomorphic classical groups G and H (subgroups of SL) may have non-isomorphic semilinear extensions. At the level of semidirect products, this corresponds to different actions of the Galois group on a given abstract group, a semidirect product depending on two groups and an action. If the extension is non-unique, there are exactly two semilinear extensions; for example, symplectic groups have a unique semilinear extension, while SU(n, q) has two extensions if n is even and q is odd, and likewise for PSU. (Wikipedia).
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points is a parallelogram by using the slope formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
How to determine the perimeter of a quadrilateral using distance formula of four points
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points is a trapezoid or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Daxin Xu - Parallel transport for Higgs bundles over p-adic curves
Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric étale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree zero over X. We will talk about an equivalence betwe
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
From playlist Cartier Operator
The p-adic Simpson correspondence and Higgs isocrystals
Titre : The p-adic Simpson correspondence and Higgs isocrystals Résumé : The p-adic Simpson correspondence of Faltings between small Higgs bundles and small generalized representations, and another approach for it by A. Abbes and M. Gros both depend on the choice of a certain smooth lifti
From playlist Conférence de mi-parcours du programme ANRThéorie de Hodge p-adique et Développements (ThéHopaD)25-27 septembre 2013
STPM - p-Adic Galois Representations and (φ,Γ)(φ,Γ)-Modules - Ruochuan Liu
Ruochuan Liu Institute for Advanced Study September 27, 2010 We will explain the equivalences between p-adic Galois representations and various types of (φ,Γ)(φ,Γ)-modules. For more videos, visit http://video.ias.edu
From playlist Mathematics
Generic global existence for the modified SQG equation - Javier Gomez-Serrano
Workshop on Recent developments in incompressible fluid dynamics Topic: Generic global existence for the modified SQG equation Speaker: Javier Gomez-Serrano Affiliation: Brown University/University of Barcelona Date: April 06, 2022 In this talk we will present a construction of global ex
From playlist Mathematics
Cartier Operator awesomeness part 1
Some basic computations with the Cartier Operator. In this video we start from the viewpoint of the Cartier operator being a simple rule.
From playlist Cartier Operator
Hatem ZAAG - A pyramid-shaped blow-up set for the 2d semilinear wave equation
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with a pyramid-shaped blow-up surface and an isolated characteristic blow-up point at the origin. Our solution is symmetric with respect to bot
From playlist Trimestre "Ondes Non linéaires" - June Conference
Asymptotic analysis of a Certain Class of Semilinear Parabolic Problem....by Ivy Carol B. Lomerio
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath Nandakumaran and Daniel Onofrei DATE: 26 August 2019 to 06 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Homogenization is a mathematical procedure to understa
From playlist Multi-scale Analysis And Theory Of Homogenization 2019
How to determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
How to determine if points are a rhombus, square or rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
SN Partial Differential Equations and Applications Webinar - Arnulf Jentzen
Join Arnulf Jentzen of University of Münster as he proves that suitable deep neural network approximations do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and thereby proves, for the first time, that a general semilinear parabolic
From playlist Talks of Mathematics Münster's reseachers
Andras Vasy - Quasilinear waves and trapping: Kerr‐de Sitter space
In this talk I will describe recent work with Peter Hintz on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr‐de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a g
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Using the slope formula to determine if points make up a rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane