involutorial
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- involutorial anti automorphism
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Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.
利用矩阵技巧和所建立的矩阵理论,给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外,还有重要的应用价值。在具有对合反自同构的正则环上,给出了四类矩阵方程组有双对称解,中心对称解,斜中心对称解,广自共轭解,斜广自共轭解,自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。
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Selfconjugate matrix, skewselfconjugate matrix, perselfconjugate matrix, skewperselfconjugate matrix, centrosymmetric matrix, skewcentrosymmetric matrix, bisymmetric matrix, and skewbisymmetric matrix over a ring with an involutorial antiautomorphism are defined. Significant criteria for matrices to be bisymmetric and skewbisymmetric are obtained.
在具有对合反自同构的环上定义了自共轭矩阵,斜自共轭矩阵,广自共轭矩阵,斜广自共轭矩阵,中心对称矩阵,斜中心对称矩阵,双对称矩阵和斜双对称矩阵,建立了双对称矩阵和斜双对称矩阵的重要判定定理。
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involutorial anti automorphism:对合反自同构
involution 对合 | involutorial anti automorphism 对合反自同构 | involutory algebra 对合代数
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involutorial crossed product:对合交叉乘积
对合反自同构 involutorial anti-automorphism | 对合交叉乘积 involutorial crossed product | 对合循环代数 involutorial cyclic algebra
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involutorial quaternion algebra:对合四元代数
对合循环代数 involutorial cyclic algebra | 对合四元代数 involutorial quaternion algebra | 对合有理代数 involutorial rational algebra
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involutorial algebra:对合代数
对合变换 involution transformation | 对合代数 involutorial algebra | 对合反自同构 involutorial anti-automorphism
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involutorial algebras:对合代数
involutive distribution | 对合分配 | involutorial algebras | 对合代数 | involutorial crossed product | 对合交叉乘积
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