Introduction of Reflection
In mathematics, a Reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of figure by a reflection is its mirror image in the axis or plane of reflection. For illustration the mirror image of the small Latin letter 'a' for a reflection with respect to a vertical axis would look like b. Its image by reflection in a horizontal axis would look like p. A reflection is an involution: when applied twice in succession every point returns to its original location and every geometrical object is restored to its original state.
The term "reflection" is sometimes used for a larger class of mappings from a Euclidean space to itself namely the non-identity isometries that are involutions. This type of isometries has a set of fixed points (the "mirror") that is an affine subspace, but possibly smaller than a hyperplane. For example a reflection through a point is an involutive isometry with just one fixed point; the image of the letter p under it would look like a d. This operation is also known as central inversion (Coxeter 1969, §7.2), and exhibits Euclidean space as a symmetric space. In Euclidean vector space the reflection in the point situated at the origin is the same as vector negation. Other illustrations include reflections in a line in three dimensional spaces. Usually, however, unqualified use of the term "reflection" means reflection in a hyperplane.
Reflection across a line in the plane
It can be defined by the formula:
Where v denotes the vector being reflected and l denotes any vector in the line being reflected in and v·l denotes the dot product of v with l.
Note: This formula can also be described as
Where the reflection of line l on a is equal to 2 times the projection of v on line l minus v. Reflections in line have the eigenvalues of 1 and -1.
Email based Reflection Homework Help -Assignment Help
Tutors at the www.tutorsglobe.com are committed to provide the best quality Reflection homework help - assignment help. They use their experience, as they have solved thousands of the Reflection assignments, which may help you to solve your complex Reflection homework. You can find solutions for all the topics come under the Reflection. The dedicated tutors provide eminence work on your Geometry Mathematics homework help and devoted to provide K-12 level Geometry Mathematics to college level Geometry Mathematics help before the deadline mentioned by the student. Reflection homework help is available here for the students of school, college and university. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Qualified and Experienced Reflection Tutors at www.tutorsglobe.com
Tutors at the www.tutorsglobe.com take pledge to provide full satisfaction and assurance in Reflection homework help. Students are getting Geometry Mathematics homework help services across the globe with 100% satisfaction. We value all our service-users. We provide email based Reflection homework help - assignment help. You can join us to ask queries 24x7 with live, experienced and qualified Geometry Mathematics tutors specialized in Reflection.
an immersion water heater is an extremely simple appliance that heats a bucket of water within 10 to 15 minutes.
tutorsglobe.com biology in human welfare assignment help-homework help by online botany tutors
tutorsglobe.com thalassemia assignment help-homework help by online genetic diseases tutors
www.tutorsglobe.com offers answering questions to economic problems associated with unemployment, theory of unemployment theory, economics assignment help-homework help by online tutors
Get quick and immediate United Nations Assignment Help service from skilled and qualified tutors to score top grades.
tutorsglobe.com atomic and ionic radii assignment help-homework help by online general characteristics of d-block elements tutors
Flip-Flops tutorial all along with the key concepts of RS Flip-flop, Setting Flip-flop, Resetting or Clearing Flip-flop, Clocked RS Flip-flop, Clocked D Flip-flop, D Latch, Clocked JK Flip-flop
Ecology of Terrestrial and aquatic animals tutorial all along with the key concepts of Ecology and Biology of Fish Species, Clupeidae, Carangidae, Polynemidae, Sciaenidae, Sparidae and Penaeid shrimps
sonar (generally an acronym for sound navigation and ranging) is a method which uses sound propagation (generally underwater, like in submarine navigation) to navigate, communicate with or detect another vessels.
Systemic Mycoses tutorial all along with the key concepts of Coccidiomycosis, Blastomycosis, Histoplasmosis, Cryptococcosis, Systemic Candidiasis, Aspergillosis and Zygomycosis
tutorsglobe.com bacterial genetics assignment help-homework help by online bacteria-structure tutors
with our introduction to statistics assignment help, you may surely get a++ grades along with unique solutions, professional advice and 24/7 support.
Avail 100% unique & plagiarism free Ageing and Health Assignment Help by industry best tutors for achieving great academic success!
tutorsglobe.com causes of cancer assignment help-homework help by online neoplasm tutors
tutorsglobe.com indifference curve assignment help-homework help by online indifference curve approach tutors
1952045
Questions Asked
3689
Tutors
1491651
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!