摘要
鉴于赋范空间L2-可和向量一定是毕达哥拉斯正交的齐次方向,但没有讨论反向的蕴含关系是否成立.通过研究毕达哥拉斯正交齐次方向和L2-可和向量的几何特征,从而证明了毕达哥拉斯正交的齐次方向一定是L2-可和向量.因此,一个单位向量是L2-可和向量当且仅当它是毕达哥拉斯正交的一个齐次方向.此外,还给出L2-可和向量和等距反射向量之间的关系.
It is proved that an L2-summand vector is necessarily a homogeneous direction of Pythagorean or- thogonality in normed linear spaces, but there is no discussion of whether the implication of the reverse is estab- lished. In view of this, we study the geometric properties of a homogeneous direction of Pythagorean orthogonality and an L2-summand vector. It is shown that a homogeneous direction of Pythagorean orthogonality is an L2-summand vector. Therefore, a unit vector is an L2-summand if and only if it is a homogeneous direction of Pythagorean or- thogonality. In addition, we study the relation between L2-summand vectors and isometric reflection vectors.
出处
《哈尔滨理工大学学报》
CAS
北大核心
2015年第5期108-110,共3页
Journal of Harbin University of Science and Technology
基金
国家自然科学基金(11371114
11171082)
关键词
毕达哥拉斯正交
L2-可和向量
齐次方向
Pythagorean orthogonality
L2-summand vector
homogeneous direction
