![](/images/graphics-bg.png)
Weakly generated vector spaces
Other Title(s)
الفضاءات المتجهية ضعيفة التوليد
Joint Authors
Hakimi, Hamzah
Jibran, Jibran
al-Taybani, Adnan
al-Khujah, Iman
Source
Damascus University Journal for the Basic Sciences
Issue
Vol. 36, Issue 2 (31 Dec. 2020), pp.261-289, 29 p.
Publisher
Publication Date
2020-12-31
Country of Publication
Syria
No. of Pages
29
Main Subjects
Abstract EN
It is important to appreciate at outset that the idea of a vector space in the algebraic abstraction and generalization of the Cartesian coordinate system introduced into the Euclidean plane, that is, a generalization of analytic geometry.
therefore, a number of interesting papers have been published on the concepts of generating sets and linearly independence.
in this paper, we study the notion of weak generation of a vector space over a field and the notion of weakly independent sets as a generalization of linearly independent sets in vector spaces.
we proved that if W X is the subspace of V weakly generated by X , then X X W, and W X X if and only if W X X .
also, if X Y are subsets of V , then W W X Y .
If X is a finite subset of V and 0X , then X is linearly independent if and only if X {0} is weakly independent.
also, we proved that the subset x of v is weakly independent if and only if each element w vx can be written as a weak linear combination of x as the only form.
finally, interesting properties and corollaries are obtained for weakly independent subsets.
American Psychological Association (APA)
al-Taybani, Adnan& Hakimi, Hamzah& al-Khujah, Iman& Jibran, Jibran. 2020. Weakly generated vector spaces. Damascus University Journal for the Basic Sciences،Vol. 36, no. 2, pp.261-289.
https://search.emarefa.net/detail/BIM-1278239
Modern Language Association (MLA)
al-Taybani, Adnan…[et al.]. Weakly generated vector spaces. Damascus University Journal for the Basic Sciences Vol. 36, no. 2 (2020), pp.261-289.
https://search.emarefa.net/detail/BIM-1278239
American Medical Association (AMA)
al-Taybani, Adnan& Hakimi, Hamzah& al-Khujah, Iman& Jibran, Jibran. Weakly generated vector spaces. Damascus University Journal for the Basic Sciences. 2020. Vol. 36, no. 2, pp.261-289.
https://search.emarefa.net/detail/BIM-1278239
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 289
Record ID
BIM-1278239