偶数阶行列和始元幻阵的构造方法
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摘要
行列和始元幻阵的构造可以分为奇数阶和偶数阶两种情况,主要研究偶数阶行列和始元幻阵的构造,并将其构造方法按照行数、列数分为四种情况:行数、列数为双偶数;行数、列数为单偶数;行数为单偶数,列数为双偶数和行数为双偶数,列数为单偶数.
In the paper,the structure of the column and initial element can be divided into two cases of odd and even order, and the construction of the even order ranks and the unreal array of the initial element is mainly studied.According to row number and column number,there are four cases. Row number and column number are double even numbers. Row number and column number are single even numbers. Row number is single even number and column number is double even number. Row number is double even number and column number is single even number.
In the paper,the structure of the column and initial element can be divided into two cases of odd and even order, and the construction of the even order ranks and the unreal array of the initial element is mainly studied.According to row number and column number,there are four cases. Row number and column number are double even numbers. Row number and column number are single even numbers. Row number is single even number and column number is double even number. Row number is double even number and column number is single even number.
引文
[1]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004.
[2]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2007.
[3]陈公宁.矩阵理论与分析[M].北京:科学出版社,2007.
[4]HORN R A,JOHNSON C R.Matrix Analysis(卷1)[M].北京:人民邮电出版社,2005.
[5]HORN R A,JOHNSON C R.Matrix Analysis(卷2)[M].北京:人民邮电出版社,2005.
[6]HORN R A,JOHNSON C R.Matrix Analysis(卷3)[M].北京:人民邮电出版社,2009.
[7]何超,何建勋.偶阶同心幻方的简明快速构造[J].华中理工大学学报,1992(4):185-188.
[8]段振华.构造偶阶幻方的一个算法[J].微电子学与计算机,1990(4):13-16,12.
[9]陈道琦.n阶幻K方的一个构造法[J].浙江大学学报,1979(4):123-138.
[10]曹燕飞,刘兴祥.构造始元幻方的广义Kronecker积法[J].河南科学,2016,34(7):1022-1025.
[11]曹燕飞,刘兴祥.3k阶拉丁幻方的构造方法[J].延安大学学报(自然科学版),2016,35(4):24-26.
[12]何敏梅,刘兴祥.4k阶始元幻方的矩阵构造法[J].河南科学,2017,35(10):1562-1566.
[13]刘春林.偶幻阵及其构造[J].徐州师范学院学报(自然科学版),1993(2):11-14.
[14]刘玉龙.广义偶幻阵及其构造[J].徐州师范学院学报(自然科学版),1994(2):8-11.
[15]强春晨.始元幻阵广义Kronecker积的保持性[D].延安:延安大学,2014.
[16]朱磊.广义平方幻阵的广义Hadamard积的保持性[D].延安:延安大学,2015.
[17]郭萍,刘兴祥.和幻阵的定义及代数性质[J].延安大学学报(自然科学版),2017,36(1):21-27.
[18]郭萍,刘兴祥,何敏梅.积幻阵的定义及矩阵性质[J].延安大学学报(自然科学版),2017,36(3):72-74.
[19]郭萍,刘兴祥,何敏梅.异元和幻阵的同构异型体及计数研究[J].江西科学,2018,36(1):11-13,30.
[2]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2007.
[3]陈公宁.矩阵理论与分析[M].北京:科学出版社,2007.
[4]HORN R A,JOHNSON C R.Matrix Analysis(卷1)[M].北京:人民邮电出版社,2005.
[5]HORN R A,JOHNSON C R.Matrix Analysis(卷2)[M].北京:人民邮电出版社,2005.
[6]HORN R A,JOHNSON C R.Matrix Analysis(卷3)[M].北京:人民邮电出版社,2009.
[7]何超,何建勋.偶阶同心幻方的简明快速构造[J].华中理工大学学报,1992(4):185-188.
[8]段振华.构造偶阶幻方的一个算法[J].微电子学与计算机,1990(4):13-16,12.
[9]陈道琦.n阶幻K方的一个构造法[J].浙江大学学报,1979(4):123-138.
[10]曹燕飞,刘兴祥.构造始元幻方的广义Kronecker积法[J].河南科学,2016,34(7):1022-1025.
[11]曹燕飞,刘兴祥.3k阶拉丁幻方的构造方法[J].延安大学学报(自然科学版),2016,35(4):24-26.
[12]何敏梅,刘兴祥.4k阶始元幻方的矩阵构造法[J].河南科学,2017,35(10):1562-1566.
[13]刘春林.偶幻阵及其构造[J].徐州师范学院学报(自然科学版),1993(2):11-14.
[14]刘玉龙.广义偶幻阵及其构造[J].徐州师范学院学报(自然科学版),1994(2):8-11.
[15]强春晨.始元幻阵广义Kronecker积的保持性[D].延安:延安大学,2014.
[16]朱磊.广义平方幻阵的广义Hadamard积的保持性[D].延安:延安大学,2015.
[17]郭萍,刘兴祥.和幻阵的定义及代数性质[J].延安大学学报(自然科学版),2017,36(1):21-27.
[18]郭萍,刘兴祥,何敏梅.积幻阵的定义及矩阵性质[J].延安大学学报(自然科学版),2017,36(3):72-74.
[19]郭萍,刘兴祥,何敏梅.异元和幻阵的同构异型体及计数研究[J].江西科学,2018,36(1):11-13,30.