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若A为整环上的n阶可逆矩阵,则X=A-1是满足方程rank■=rank(A)的唯一矩阵.把它推广到满足Rao条件的整环上得到关于矩阵A的Moore-Penrose逆A+的刻画. 相似文献
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逆矩阵概念与线性映射的逆映射概念紧密相关.从线性映射的逆映射这个视角引入可逆矩阵概念对于理解可逆矩阵的本质和逆矩阵的求法具有重要的意义. 相似文献
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用数学归纳法推出了可逆矩阵的高次伴随矩阵的公式,并结合可逆矩阵的基本公式得出了可逆矩阵的高次伴随矩阵的行列式和逆矩阵,给出了可逆矩阵的高次伴随矩阵的特征值和特征向量的表示公式,最后讨论了若干个可逆矩阵的乘积的高次伴随矩阵. 相似文献
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刻画了某类特殊可换无零因子反环上保持矩阵{1}一逆的可逆线性算子,并将此结果推广到此类无零因子反环的任意直积上.推广了某些文献的一些结果. 相似文献
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基于Moore-Penrose逆和弱Core逆该文提出了Moore-Penrose弱Core逆(MPWC逆)的概念.分别从代数和几何角度对它进行刻画,给出了MPWC逆与非奇异加边矩阵之间的关系,应用Hartwig-Spindelb?ck分解和Core-EP分解给出了MPWC逆的性质、刻画及其扰动分析,最后给出了矩阵的MPWC逆是EP矩阵的等价条件. 相似文献
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一类广义范德蒙矩阵的求逆公式及递推公式 总被引:1,自引:0,他引:1
陆全 《数学的实践与认识》2004,34(7):132-135
利用线性方程组给出了一类广义范德蒙矩阵可逆的条件及逆矩阵的矩阵表示式 ,并给出了求逆的递推公式 . 相似文献
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We study birth and death processes with linear rates λn = n + α + c + 1, μn + 1 = n + c, n 0 and μ0 is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ0 = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations. 相似文献
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We study rings in which every ideal is a finitely generated multiplication right ideal. 相似文献
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V. V. Makeev 《Journal of Mathematical Sciences》1998,91(6):3518-3525
Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are
proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ3, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved
that every compact convex set in ℝ3 (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints
of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder
with directrix P. Bibliography: 29 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298.
Translated by B. M. Bekker. 相似文献
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Neil Hindman 《Journal of Combinatorial Theory, Series A》1984,37(1):46-60
A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions. 相似文献
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The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education. 相似文献