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- Row_equivalence abstract "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.".
- Row_equivalence wikiPageExternalLink DownloadChapters.html.
- Row_equivalence wikiPageID "5896724".
- Row_equivalence wikiPageRevisionID "565007303".
- Row_equivalence hasPhotoCollection Row_equivalence.
- Row_equivalence subject Category:Linear_algebra.
- Row_equivalence subject Category:Matrices.
- Row_equivalence type Abstraction100002137.
- Row_equivalence type Arrangement107938773.
- Row_equivalence type Array107939382.
- Row_equivalence type Group100031264.
- Row_equivalence type Matrices.
- Row_equivalence type Matrix108267640.
- Row_equivalence comment "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.".
- Row_equivalence label "Matrices l-équivalentes".
- Row_equivalence label "Row equivalence".
- Row_equivalence sameAs Matrices_l-équivalentes.
- Row_equivalence sameAs m.0fcf01.
- Row_equivalence sameAs Q3444264.
- Row_equivalence sameAs Q3444264.
- Row_equivalence sameAs Row_equivalence.
- Row_equivalence wasDerivedFrom Row_equivalence?oldid=565007303.
- Row_equivalence isPrimaryTopicOf Row_equivalence.