Constructing position vectors for the intersection of two and three linear varieties

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-08 DOI:10.1016/j.laa.2025.05.003

M.A. Facas Vicente , José Vitória

引用次数: 0

Abstract

Position vectors are much useful in several fields, such as Differential Geometry, Mechanics and in Engineering, in particular in Dimensional Metrology. We generalize, for linear varieties in

R^{n}

, the corresponding results known for the Euclidean ordinary space. The Moore-Penrose inverse of matrices plays an important rôle in this paper. Generalizations for three linear varieties of the Anderson-Duffin formulae are presented. We establish several formulae for a position vector of the intersection of linear varieties. Some characterization of the position vector is provided in terms of centres of spheres. Results, in the context of commuting projections, are given as well.

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构造两个和三个线性变量交点的位置向量

位置向量在微分几何、力学和工程，尤其是尺寸计量等领域都很有用。我们推广，对于Rn中的线性变换，相应的结果在欧氏普通空间中是已知的。矩阵的Moore-Penrose逆在本文中起着重要作用rôle。给出了Anderson-Duffin公式的三个线性变体的推广。我们建立了线性变分交点的位置向量的几个公式。用球的中心给出了位置矢量的一些表征。结果，在通勤预测的背景下，也给出了。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.