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41.
A particular orthogonal map on a finite-dimensional real quadratic vector space (V,?Q) with a non-degenerate quadratic form Q of any signature (p,?q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra C?(V*,?Q) of linear functionals (multiforms) acting on the universal Clifford algebra C?(V,?Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of C?(V,?Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of C?(V,?Q). We also give an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [R. Ab?amowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras II: Stabilizer groups of primitive idempotents, Linear Multilinear Algebra, to appear]. 相似文献
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43.
A number of characterizations involving column and null spaces of various functions of a pair of oblique projectors are established. Particular attention is paid to properties of a product of the two projectors, but other functions of the pair (such as sum, difference or sum and difference of products) are considered as well. In many cases, the results obtained generalize those already known to be valid for orthogonal projectors. 相似文献
44.
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
45.
In their paper [Y. Tian, G.P.H. Styan, Rank equalities for idempotent and involutory matrices. Linear Algebra Appl. 335 (2001) 101-117], Tian and Styan established several rank equalities involving a pair of idempotent matrices P and Q. Subsequently, these results are reinvestigated from the point of view of the following question: provided that idempotent P, Q are Hermitian, which relationships given in the aforementioned paper remain valid when ranks are replaced with column spaces? Simultaneously, some related results are established, which shed additional light on the links between subspaces attributed to various functions of a pair of orthogonal projectors. 相似文献
46.
给出了纯正半群S的强同余格上同余T的一些判别性质,证明了S上所有基础强同余所构成的集合FCP(S)是CP(S)的完备子格,最后讨论了由纯正半群的正规子半群决定的交完备子格的结构及由“求核”运算确定的(交完备格)同余K的若干性质,还顺带讨论了群同余格. 相似文献
47.
48.
素GPI-环广义形心扩张的本原性 总被引:1,自引:0,他引:1
类似于中心扩张,本文引入了广义形心扩张的概念,且研究了广义形心扩张的本原性。 相似文献
49.
51.IntroductionandPreIiminariesThemonoidofendomorphismsofagraph,inparticular,thatofstrongendomorphismsofagraph,hasbeentheobjectofresearchesinthetheoryofsemigroupsforquitesometime(cf.Llj-Lloj).LlJandL2jcanserveasasurvey.Theaimoftheseresearchesistocon-tributetothealgebraicanalysisofgraphs.Thesubjectyieldssomeinterestsincetheresultsoftheseresearchesmayopenvastpossibilitiesforapplicationsofsemigrouptheorytographtheo-ry.InL1]andL3j,ithasbeenprovedthatforfinitegraphG,sEnd(G),themonoidofstrongen… 相似文献
50.
E. M. Vechtomov 《Mathematical Notes》1997,62(5):575-580
The latticeA(X) of all possible subalgebras of the ring of all continuous ℝ-valued functions defined on an ℝ-separated spaceX is considered. A topological space is said to be a Hewitt space if it is homeomorphic to a closed subspace of a Tychonoff
power of the real line ℝ. The main achievement of the paper is the proof of the fact that any Hewitt spaceX is determined by the latticeA(X). An original technique of minimal and maximal subalgebras is applied. It is shown that the latticeA(X) is regular if and only ifX contains at most two points.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 687–693, November, 1997.
Translated by A. I. Shtern 相似文献