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O que (quem) é symplectic plane - definição

Symplectic transformation; Symplectic operator

Symplectic geometry

BRANCH OF DIFFERENTIAL GEOMETRY AND DIFFERENTIAL TOPOLOGY

Symplectic Geometry; Symplectic structure; Symplectic topology

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry was founded by the Russian mathematician Vladimir Arnold and has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.

https://en.wikipedia.org/wiki/Symplectic_geometry

Supplementary Ideographic Plane

CONTINUOUS GROUP OF 65536 CODE POINTS IN THE UNICODE CODED CHARACTER SET

Basic multilingual plane; Basic Multilingual Plane; Supplementary Multilingual Plane; Plane One; Plane Zero; Plane Fifteen; Plane Sixteen; Supplementary Ideographic Plane; Plane Two; Supplementary Special-purpose Plane; Plane Fourteen; Plane 0; Plane 1; Plane 2; Plane 14; Plane 15; Plane 16; Astral character; Mapping of Unicode character planes; Unicode plane; Supplementary characters; Unicode planes; Tertiary Ideographic Plane; Private Use Plane; Astral plane (Unicode); Plane 15 (Unicode); Plane 16 (Unicode); Private use plane; Private use plane (Unicode); UCS-PUP15; PUP15; PUP16; UCS-PUP16; PUP15 (Unicode); PUP16 (Unicode); Supplementary plane; Unicode BMP; Private Use Planes; Plane 4; Plane 5; Plane 6; Plane 7; Plane 8; Plane 9; Plane 10; Plane 11; Plane 12; Plane 13; Supplemental Multilingual Plane; Supplemental Ideographic Plane; Supplemental Special-purpose Plane; Plane (unicode)

<text, standard> (SIP) The third plane (plane 2) defined in Unicode/ISO 10646, designed to hold all the ideographs descended from Chinese writing (mainly found in Vietnamese, Korean, Japanese and Chinese) that aren't found in the {Basic Multilingual Plane}. The BMP was supposed to hold all ideographs in modern use; unfortunately, many Chinese dialects (like Cantonese and Hong Kong Chinese) were overlooked; to write these, characters from the SIP are necessary. This is one reason even non-academic software must support characters outside the BMP. Unicode home (http://unicode.org). (2002-06-19)

Plane (geometry)

FLAT, TWO-DIMENSIONAL SURFACE

Infinite Plane; Infinite plane; Plane coordinates; Plane coordinate; 2-dimensional space; Euclidean 2-space; Euclidean two-dimensional space; Two-dimensional Euclidean space; Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends indefinitely.In Euclidean geometry it extends infinitely, but in, e.

https://en.wikipedia.org/wiki/Plane_(geometry)

Wikipédia

Symplectic matrix

In mathematics, a symplectic matrix is a $2n\times 2n$ matrix $M$ with real entries that satisfies the condition

where $M^{\text{T}}$ denotes the transpose of $M$ and $\Omega$ is a fixed $2n\times 2n$ nonsingular, skew-symmetric matrix. This definition can be extended to $2n\times 2n$ matrices with entries in other fields, such as the complex numbers, finite fields, p-adic numbers, and function fields.

Typically $\Omega$ is chosen to be the block matrix

where

I_{n}

is the

n\times n

identity matrix. The matrix

\Omega

has determinant

+1

and its inverse is

\Omega ^{-1}=\Omega ^{\text{T}}=-\Omega

.

https://en.wikipedia.org/wiki/Symplectic matrix