• Weak Linear Independence of Vector Spaces

    Hamza Hakmi1, Eaman Al-Khouja2, Adnan Al-Taybani2

    1. Department of Mathematics, Faculty of Sciences, Damascus University, Damascus, Syria.
    2. Department of Mathematics, Faculty of Sciences, Al-Baath University, Homs, Syria.

    Abstract: 

    The problem of generation and oneness considered for expressing about an element is very important and has a big effect in mathematics in general and in algebra in special for example in vector spaces, every element from this space is expressed in a unique way as a linear combination of elements of its base.
    In this paper, we introduce and study new concepts in vector space over a field, to express every element from this space in a unique way called weak linear combination.

    Keywords: Weak linear combination, Weak generation, Weak linear independence, Full linear dependence, Weak base, Independent weak base.

    Pages: 157 – 181 | Full PDF Paper