共查询到17条相似文献,搜索用时 187 毫秒
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解决了幂等和幂零阵的伴随阵的反问题,把Sherman-Morrison公式[1]推广到求伴随阵的情形,并给出了一类伴随还原阵的简单求法. 相似文献
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关于幂等阵的相似与线性组合 总被引:3,自引:0,他引:3
证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩;给出了幂等阵的相似标准型;讨论了两个幂等阵的线性组合仍是幂等阵的充要条件. 相似文献
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幂等阵幂零阵多项式可逆的充要条件及一般方阵多项式可逆性的判定 总被引:5,自引:0,他引:5
1 幂等阵多项式设A∈Fn×n 为一幂等矩阵 ,由于A2 =A ,所以任取f(x) ∈F[x].f(A)总可以化为kA+lIn的形式 (k,l∈F ,In 为n阶单位阵 ) .对此我们有定理 1 若A为n阶非零幂等矩阵 ,k≠ 0 ,l≠ 0 ,则kA +lIn 可逆 k≠-l.证 充分性因为l≠ 0 ,k≠-l,所以l(k +l)In 可逆又 (kA +lIn) [-kA+(k+l)In]=-k2 A2 +k2 A+klA-klA +l(k+l)In=l(k+l)In所以kA+lIn 可逆 .必要性若kA+lIn 可逆 ,而k=-l,则由A(kA+lIn) =kA2 +lA =0 nn,可知R(A) +R(… 相似文献
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讨论了反幂等阵线性组合的幂等性,指出可对角化矩阵可表示为反幂等阵的线性组合,并由此得到了由非奇异矩阵构造两两正交且可交换的反幂等阵的一种方法. 相似文献
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幂等右侧Quantale上的幂零矩阵 总被引:2,自引:0,他引:2
讨论幂等右侧Quantale上的幂零矩阵的若干性质,给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件,得到了幂零矩阵的幂零指数的刻画定理。 相似文献
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我们讨论了p-幂零限制李超代数的一些性质,分别给出了p-幂零和幂零限制李超代数的几个充分必要条件,并讨论了幂零与p-幂零之间的关系.最后,证明了幂零限制李超代数的一些性质. 相似文献
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域上三角矩阵空间保幂等与立方幂等的加法单映射 总被引:2,自引:0,他引:2
本文刻划了特征不为2的域上三角矩阵空间保幂等加法单映射,并由此获得了特征不为2及3的域上三角矩阵空间保立方幂等加法单映射的形式. 相似文献
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零代数在什么条件下是幂零的?这是一个重要问题。类似地,我们提出另一问题,对于幂零元生成的子代数在什么条件下是幂零的?一个幂零元生成的子代数显然是幂零的,两个幂零元生成的子代数一般不是诣零的。本文得到一个肯定结果: 相似文献
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实幂等矩阵的伴随矩(英) 总被引:4,自引:2,他引:4
AnAdjointMatrixofaRealIdempotentMatrixJinBaiKim(Dept.ofMath.,WestVirginiaUniversityMorgantown,WV26506,USA)HeeSikKim(Dept.ofMa... 相似文献
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Aleksandra S.Kosti 《Algebra Colloquium》2021,28(4):625-634
Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n × n matrix A over R is expressible as a sum A =E1 +…+ Es + N of (commuting) idempotent matrices Ei and a nilpotent matrix N. 相似文献
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This paper deals with the structure of semiprime rings for which the indices of the nilpotent elements are bounded. It is shown that the complete right ring of quotients of such a ring is a regular, right self-injective ring in which each finitely generated ideal is generated by a central idempotent. The indices of the nilpotent elements of the factor ring of such a ring with respect to a minimal prime ideal do not exceed the upper bound of the indices of the nilpotent elements of the original ring. A criterion for the regularity (in the sense of von Neumann) of such rings is obtained. Also investigated are right completely idempotent rings with bounded indices of nilpotent elements (it is shown, in particular, that each nonzero ideal of such a ring contains a nonzero central idempotent).Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 237–249, 1988. 相似文献
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K. A. Zhevlakov 《Mathematical Notes》1972,12(2):507-509
It is shown that a locally nilpotent ring with maximality condition for two-sided ideals is nilpotent. The restriction on the characteristic in one of the author's previously published theorems is lifted. A one-sided nil-ideal of an alternative ring, satisfying the maximality condition for right ideals, is a nilpotent ring. An example is constructed of a commutative locally nilpotent ring A with maximality condition for ideals which is idempotent: A = A2.The article was prepared for print by the author and submitted after his death which took place on February 24, 1972.Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 121–126, August, 1972. 相似文献
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We will show that skew polynomial rings in several variables over locally nilpotent rings cannot contain nonzero idempotent elements. We will also prove that such rings are Brown–McCoy radical. 相似文献
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General recurrence formulas for matrix elements of representations of Lie groups on enveloping algebras are given. In particular, we show the connection with the exponential of the adjoint representation which is an important feature of the construction. The methods are applicable for groups of arbitrary dimension and have been implemented using MAPLE. A three-step nilpotent group and SU(3) provide examples of the theory. 相似文献