| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/unitlib/data/ (MySQL Server Version 8.1-8.4©) |
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Quellcode-Bibliothek ffmat.xml Sprache: XML |
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## #W ffmat.xml #Y Copyright (C) 2014-2022 ## ## Licensing information can be found in the README file of this package. ## ############################################################################# <#GAPDoc Label="RowSpaceBasis"> <ManSection> <Attr Name="RowSpaceBasis" Arg="m" Label="for a matrix over finite field"/> <Attr Name="RowSpaceTransformation" Arg="m" Label="for a matrix over finite field"/> <Attr Name="RowSpaceTransformationInv" Arg="m" Label="for a matrix over finite field"/> <Description> If <A>m</A> is a matrix object over a finite field, then to compute the value of any of the above attributes, a canonical basis for the row space of <A>m</A> is computed along with an invertible matrix <C>RowSpaceTransformation</C> such that <C>m * RowSpaceTransformation(m) = RowSpaceBasis(m)</C>. <C>RowSpaceTransformationInv(m)</C> is the inverse of <C>RowSpaceTransformation(m)</C>. <Example><![CDATA[ gap> x := Matrix(GF(4), Z(4) ^ 0 * [[1, 1, 0], [0, 1, 1], [1, 1, 1]]); [ [ Z(2)^0, Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, Z(2)^0 ], [ Z(2)^0, Z(2)^0, Z(2)^0 ] ] gap> RowSpaceBasis(x); <rowbasis of rank 3 over GF(2^2)> gap> RowSpaceTransformation(x); [ [ 0*Z(2), Z(2)^0, Z(2)^0 ], [ Z(2)^0, Z(2)^0, Z(2)^0 ], [ Z(2)^0, 0*Z(2), Z(2)^0 ] ]]]></Example> </Description> </ManSection> <#/GAPDoc> <#GAPDoc Label="RightInverse"> <ManSection> <Attr Name="RightInverse" Arg="m" Label="for a matrix over finite field"/> <Attr Name="LeftInverse" Arg="m" Label="for a matrix over finite field"/> <Returns>A matrix over a finite field.</Returns> <Description> These attributes contain a semigroup left-inverse, and a semigroup right-inverse of the matrix <A>m</A> respectively. <Example><![CDATA[ gap> x := Matrix(GF(4), Z(4) ^ 0 * [[1, 1, 0], [0, 0, 0], [1, 1, 1]]); [ [ Z(2)^0, Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0 ] ] gap> LeftInverse(x); [ [ Z(2)^0, Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, 0*Z(2), Z(2)^0 ] ] gap> Display(LeftInverse(x) * x); 1 1 . . . . . . 1 ]]></Example> </Description> </ManSection> <#/GAPDoc> ¤ Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.0.12Bemerkung: (vorverarbeitet) ¤*Bot Zugriff |
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