About: Triangular matrix

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

About: Triangular matrix Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero.

Attributes	Values
rdf:type	Thing
rdfs:label	Triangular matrix (en)
rdfs:comment	In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. (en)
rdfs:seeAlso	Affine group Diagonalizable matrix
sameAs	Triangular matrix Triangular matrix
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Citation dbt:Citation_needed dbt:Citation_style dbt:Distinguish dbt:For dbt:Harv dbt:Main dbt:Refbegin dbt:Refend dbt:Reflist dbt:See_also dbt:Visible_anchor dbt:Matrix_classes
Subject	Matrices Numerical linear algebra
gold:hypernym	Kind
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Triangular_matrix?oldid=1069328822&ns=0
Wikipage page ID	374222 (xsd:integer)
page length (characters) of wiki page	19888 (xsd:nonNegativeInteger)
Wikipage revision ID	1069328822 (xsd:integer)
has abstract	In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Triangular_matrix
is differentFrom of	Triangular array
is rdfs:seeAlso of	Diagonalizable matrix
is Wikipage redirect of	Forward substitution Back substitution Backsubstitution Unitriangular Unitriangular matrix Back-substitution Triangular matrices Triangularisability Triangularizability Lower-triangular matrix Lower triangular Lower triangular form Lower triangular matrix Strictly upper triangular Strictly upper triangular matrix Triangular factor Triangular form Triangularizable Simultaneously triangularizable Left triangular matrix Right triangular matrix Gauss matrix Strictly lower triangular matrix Trapezoidal matrix Upper-triangular Upper-triangular matrix Upper triangular Upper triangular form Upper triangular matrices Upper triangular matrix Unit triangular matrix
is Link from a Wikipage to another Wikipage of	Forward substitution List of terms relating to algorithms and data structures List of triangle topics NAS Parallel Benchmarks Normal matrix Numerical linear algebra Numerical methods for linear least squares Adjugate matrix Algebra representation BKL singularity Back substitution Backsubstitution Band matrix Basic Linear Algebra Subprograms Block reflector Bootstrapping (finance) Borel subgroup Moore–Penrose inverse Back-substitution Categorical algebra Central series Frequency selective surface Generalized flag variety Generalized minimal residual method Givens rotation Jacobson radical Jordan matrix Jordan normal form Divided differences Double coset Kuiper's theorem Metabelian group Characteristic polynomial Chinese mathematics Cholesky decomposition Crout matrix decomposition Definite matrix

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software