交换半环上矩阵行列式的性质
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摘要
本文主要研究了交换半环上矩阵乘积行列式的性质。讨论了行列式的乘积与乘积的行列式间的关系,并进一步给出了伴随阵的乘积与乘积的伴随阵之间的关系。
This paper mainly investigates the properties of determinants for matrix multiplications over commutative semirings. It discusses the relationships between the determinant of matrix multiplications and the multiplication of determinants for matrices, and shows the relationships between the multiplication of adjoint matrices and the adjoint matrix of matrix multiplications.
This paper mainly investigates the properties of determinants for matrix multiplications over commutative semirings. It discusses the relationships between the determinant of matrix multiplications and the multiplication of determinants for matrices, and shows the relationships between the multiplication of adjoint matrices and the adjoint matrix of matrix multiplications.
引文
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[2] Poplin P L,Hartwig R E.Determinantal identities over commutative semirings[J].Linear Algebra and Its Applications,2007,387:99～132.
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[4] Perfilieva I,Kupka J.Kronecker-capelli theorem in semilinear spaces[C]//Ruan D,Li T R,Xu Y,Chen G Q,Kerre E E.Computational intelligence:Foundations and applications.World Scientific,Emei,Chengdu,China,2010:43～51.
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[6] Tan Y J.On invertible matrices over commutative semirings[J].Linear and Multilinear Algebra,2013,61:710～724.
[7] Wang X P,Shu Q Y.Bideterminant and rank of matrix[J].Soft Computing,2014,18:729～742.
[8] Shu Q Y,Wang X P.The applications of the bideterminant of a matrix over commutative semirings[J].Linear and Multilinear Algebra,2017,65:1462～1478.
[9] Golan J S.Semirings and their applications[M].Dordrecht/Boston/London:Kluwer Academic Publishers,1999.
[10] Di Nola A,Lettieri A,Perfilieva I,Novak V.Algebraic analysis of fuzzy systems[J].Fuzzy Sets and Systems,2007,158:1～22.
[11] Reutenauer C,Straubing H.Inversion of matrices over a commutative semring[J].J.Algebra,1984,88:350～360.
[12] Shu Q Y,Wang X P.Standard orthogonal vectors in semilinear spaces and their applications[J].Linear Algebra and Its Applications,2012,437:2733～2754.
[13] Zhao S,Wang X P.Invertible matrices and semilinear spaces over commutative semirings[J].Information Sciences,2010,180:5115～5124.
[14] Shu Q Y,Wang X P.The cardinality of bases in semilinear spaces over commutative semirings[J].Linear Algebra and its Applications,2014,459:83～100.
[2] Poplin P L,Hartwig R E.Determinantal identities over commutative semirings[J].Linear Algebra and Its Applications,2007,387:99～132.
[3] Gondran M,Minoux M.Graphs,dioids and semirings[M].New York:Springer-Verlag,2008.
[4] Perfilieva I,Kupka J.Kronecker-capelli theorem in semilinear spaces[C]//Ruan D,Li T R,Xu Y,Chen G Q,Kerre E E.Computational intelligence:Foundations and applications.World Scientific,Emei,Chengdu,China,2010:43～51.
[5] Tan Y J.On invertible matrices over antirings[J].Linear Algebra Appl,2007,423:428～444.
[6] Tan Y J.On invertible matrices over commutative semirings[J].Linear and Multilinear Algebra,2013,61:710～724.
[7] Wang X P,Shu Q Y.Bideterminant and rank of matrix[J].Soft Computing,2014,18:729～742.
[8] Shu Q Y,Wang X P.The applications of the bideterminant of a matrix over commutative semirings[J].Linear and Multilinear Algebra,2017,65:1462～1478.
[9] Golan J S.Semirings and their applications[M].Dordrecht/Boston/London:Kluwer Academic Publishers,1999.
[10] Di Nola A,Lettieri A,Perfilieva I,Novak V.Algebraic analysis of fuzzy systems[J].Fuzzy Sets and Systems,2007,158:1～22.
[11] Reutenauer C,Straubing H.Inversion of matrices over a commutative semring[J].J.Algebra,1984,88:350～360.
[12] Shu Q Y,Wang X P.Standard orthogonal vectors in semilinear spaces and their applications[J].Linear Algebra and Its Applications,2012,437:2733～2754.
[13] Zhao S,Wang X P.Invertible matrices and semilinear spaces over commutative semirings[J].Information Sciences,2010,180:5115～5124.
[14] Shu Q Y,Wang X P.The cardinality of bases in semilinear spaces over commutative semirings[J].Linear Algebra and its Applications,2014,459:83～100.