About: Iwasawa decomposition

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Iwasawa decomposition Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Matrix108267640, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/AEi4da3Wx8

In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method.

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:WikicatMatrices yago:Abstraction100002137 yago:Arrangement107938773 yago:Array107939382 yago:Group100031264 yago:Matrix108267640
rdfs:label	Iwasawa-Zerlegung (de) Iwasawa decomposition (en) Décomposition d'Iwasawa (fr) 이와사와 분해 (ko) 岩泽分解 (zh)
rdfs:comment	Die Iwasawa-Zerlegung halbeinfacher Lie-Gruppen verallgemeinert die Tatsache, dass sich jede quadratische Matrix auf eindeutige Weise als Produkt aus einer orthogonalen Matrix und einer oberen Dreiecksmatrix darstellen lässt. Sie ist nach Kenkichi Iwasawa (1949) benannt, der sie für reelle halbeinfache Liegruppen einführte. (de) In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method. (en) La décomposition d'Iwasawa d'un groupe de Lie semi-simple est une généralisation de la décomposition d'un élément du groupe spécial linéaire SL(n, ℝ) comme produit KAN (de façon unique) d'un élément K du groupe spécial orthogonal SO(n, ℝ), d'une matrice diagonale A à coefficients diagonaux positifs (et dont le produit est nécessairement égal à 1), et d'une matrice triangulaire supérieure N dont les coefficients diagonaux valent 1. (fr) 리 군 이론에서, 이와사와 분해([岩澤]分解, 영어: Iwasawa decomposition)는 그람-슈미트 과정을 반단순 리 군에 일반화하여, 리 군의 원소를 멱영 성분·가환 성분·콤팩트 성분으로 나누는 분해이다.:197–204 (ko) 数学中，的岩泽分解 KAN 推广了实方阵能写成一个正交矩阵和上三角矩阵的乘积（格拉姆-施密特正交化之推论）。以创立者日本数学家岩泽健吉命名。 (zh)
dcterms:subject	Lie groups
Wikipage page ID	1139148 (xsd:integer)
Wikipage revision ID	1116494073 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-Archimedean field Algebraic torus Ring of integers Lie group Complexification Mathematics Lie algebra Symplectic group Mathematician Maximal compact subgroup Lie groups Gram–Schmidt process QR decomposition Japan Kenkichi Iwasawa Dimension Orthogonal matrix Cartan decomposition Real matrix Semisimple Lie group Root system of a semi-simple Lie algebra Upper triangular matrix Cartan involution Lie group decompositions Unipotent group
sameAs	Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition Iwasawa decomposition
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Cite_book dbt:Reflist
first	A.S. (en) A.I. (en)
id	Iwasawa_decomposition&oldid=21877 (en)
last	Fedenko (en) Shtern (en)
title	Iwasawa decomposition (en)
has abstract	Die Iwasawa-Zerlegung halbeinfacher Lie-Gruppen verallgemeinert die Tatsache, dass sich jede quadratische Matrix auf eindeutige Weise als Produkt aus einer orthogonalen Matrix und einer oberen Dreiecksmatrix darstellen lässt. Sie ist nach Kenkichi Iwasawa (1949) benannt, der sie für reelle halbeinfache Liegruppen einführte. (de) In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method. (en) La décomposition d'Iwasawa d'un groupe de Lie semi-simple est une généralisation de la décomposition d'un élément du groupe spécial linéaire SL(n, ℝ) comme produit KAN (de façon unique) d'un élément K du groupe spécial orthogonal SO(n, ℝ), d'une matrice diagonale A à coefficients diagonaux positifs (et dont le produit est nécessairement égal à 1), et d'une matrice triangulaire supérieure N dont les coefficients diagonaux valent 1. (fr) 리 군 이론에서, 이와사와 분해([岩澤]分解, 영어: Iwasawa decomposition)는 그람-슈미트 과정을 반단순 리 군에 일반화하여, 리 군의 원소를 멱영 성분·가환 성분·콤팩트 성분으로 나누는 분해이다.:197–204 (ko) 数学中，的岩泽分解 KAN 推广了实方阵能写成一个正交矩阵和上三角矩阵的乘积（格拉姆-施密特正交化之推论）。以创立者日本数学家岩泽健吉命名。 (zh)
prov:wasDerivedFrom	wikipedia-en:Iwasawa_decomposition?oldid=1116494073&ns=0
page length (characters) of wiki page	5577 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Iwasawa_decomposition
is Link from a Wikipage to another Wikipage of	Lie group decomposition Iwasawa Complexification (Lie group) Gelfand pair Furstenberg boundary Glossary of Lie groups and Lie algebras Harish-Chandra's Ξ function Zonal spherical function Maximal compact subgroup Gram–Schmidt process Jordan–Chevalley decomposition Kostant's convexity theorem Principal series representation QR decomposition Covering group Kenkichi Iwasawa Symmetric cone Kan Quantum group Restricted root system Superrigidity Plancherel theorem for spherical functions
is Wikipage disambiguates of	Iwasawa
is foaf:primaryTopic of	wikipedia-en:Iwasawa_decomposition

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 54 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software