About: Row equivalence

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In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m × n matrices are row equivalent if and only if they have the same row space. The concept is most commonly applied to matrices that represent systems of linear equations, in which case two matrices of the same size are row equivalent if and only if the corresponding homogeneous systems have the same set of solutions, or equivalently the matrices have the same null space.

Attributes	Values
rdf:type	yago:WikicatMatrices yago:Abstraction100002137 yago:Arrangement107938773 yago:Array107939382 yago:Group100031264 yago:Matrix108267640 organisation
rdfs:label	Matrices l-équivalentes (fr) Row equivalence (en)
rdfs:comment	En algèbre linéaire, deux matrices sont l-équivalentes (ou ligne-équivalentes) si on peut passer de l'une à l'autre par des opérations élémentaires sur les lignes. Si A et B sont deux matrices, cette condition se réécrit comme : il existe une matrice inversible tel que . (fr) In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m × n matrices are row equivalent if and only if they have the same row space. The concept is most commonly applied to matrices that represent systems of linear equations, in which case two matrices of the same size are row equivalent if and only if the corresponding homogeneous systems have the same set of solutions, or equivalently the matrices have the same null space. (en)
dct:subject	Equivalence (mathematics) Matrices Linear algebra
Wikipage page ID	5896724 (xsd:integer)
Wikipage revision ID	1124360784 (xsd:integer)
Link from a Wikipage to another Wikipage	Basis (linear algebra) Equivalence (mathematics) Matrix (mathematics) Systems of linear equations Linear algebra Identity matrix Pivot element Matrices Tilde Linear combination Linear algebra Equivalence relation Graduate Texts in Mathematics Matrix equivalence Row echelon form Rank (linear algebra) Invertible matrix Reduced row echelon form Dimension Orthogonal complement Matrix similarity System of linear equations Elementary row operations Row reduction Row space Null space
Link from a Wikipage to an external page	http://www.matrixanalysis.com/DownloadChapters.html https://web.archive.org/web/20010301161440/http:/matrixanalysis.com/DownloadChapters.html
sameAs	Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence Row equivalence
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Cn dbt:Main dbt:More_footnotes dbt:Reflist dbt:Short_description dbt:Wikibooks
has abstract	En algèbre linéaire, deux matrices sont l-équivalentes (ou ligne-équivalentes) si on peut passer de l'une à l'autre par des opérations élémentaires sur les lignes. Si A et B sont deux matrices, cette condition se réécrit comme : il existe une matrice inversible tel que . (fr) In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m × n matrices are row equivalent if and only if they have the same row space. The concept is most commonly applied to matrices that represent systems of linear equations, in which case two matrices of the same size are row equivalent if and only if the corresponding homogeneous systems have the same set of solutions, or equivalently the matrices have the same null space. Because elementary row operations are reversible, row equivalence is an equivalence relation. It is commonly denoted by a tilde (~). There is a similar notion of column equivalence, defined by elementary column operations; two matrices are column equivalent if and only if their transpose matrices are row equivalent. Two rectangular matrices that can be converted into one another allowing both elementary row and column operations are called simply equivalent. (en)
gold:hypernym	Equivalent
prov:wasDerivedFrom	wikipedia-en:Row_equivalence?oldid=1124360784&ns=0
page length (characters) of wiki page	6229 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Row_equivalence
is Link from a Wikipage to another Wikipage of	Matrix equivalence Row echelon form Invertible matrix Outline of linear algebra Equivalent Matrix Row equivalent Column equivalence
is Wikipage redirect of	Equivalent Matrix Row equivalent Column equivalence
is foaf:primaryTopic of	wikipedia-en:Row_equivalence

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