Search results
Results from the WOW.Com Content Network
Point Q is the reflection of point P through the line AB. In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.
Weak forms of the reflection principle are theorems of ZF set theory due to Montague (1961), while stronger forms can be new and very powerful axioms for set theory. The name "reflection principle" comes from the fact that properties of the universe of all sets are "reflected" down to a smaller set.
In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic continuation.It states that if an analytic function is defined on the upper half-plane, and has well-defined (non-singular) real values on the real axis, then it can be extended to the conjugate function on the lower half-plane.
The morphism is called the A-reflection arrow. (Although often, for the sake of brevity, we speak about A B {\displaystyle A_{B}} only as being the A -reflection of B ). This is equivalent to saying that the embedding functor E : A ↪ B {\displaystyle E\colon \mathbf {A} \hookrightarrow \mathbf {B} } is a right adjoint.
In mathematics, reflection through the origin refers to the point reflection of Euclidean space R n across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by − 1 {\displaystyle -1} , and can also be written as − I {\displaystyle -I} , where I ...
When K is the field of real numbers, a pseudoreflection has matrix form diag(1, ... , 1, -1). A pseudoreflection with such matrix form is called a real reflection.If the space on which this transformation acts admits a symmetric bilinear form so that orthogonality of vectors can be defined, then the transformation is a true reflection.
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation . It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
An example of a left quasi-reflexive relation is a left Euclidean relation, which is always left quasi-reflexive but not necessarily right quasi-reflexive, and thus not necessarily quasi-reflexive. An example of a coreflexive relation is the relation on integers in which each odd number is related to itself and there are no other relations. The ...