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    vector space


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    m11 vector space

    مُساهمة من طرف teacher في الخميس 24 يوليو 2008, 3:23 pm

    A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is -dimensional Euclidean space , where every element is represented by a list of real numbers, scalars are real numbers, addition is componentwise, and scalar multiplication is multiplication on each term separately.

    For a general vector space, the scalars are members of a field , in which case is called a vector space over .
    Euclidean -space is called a real vector space, and is called a complex vector space.
    In order for to be a vector space, the following conditions must hold for all elements and any scalars :
    1. Commutativity:


    2. Associativity of vector addition:


    3. Additive identity: For all ,


    4. Existence of additive inverse: For any , there exists a such that


    5. Associativity of scalar multiplication:


    6. Distributivity of scalar sums:


    7. Distributivity of vector sums:


    8. Scalar multiplication identity:


    Let be a vector space of dimension over the field of elements (where is necessarily a power of a prime number). Then the number of distinct nonsingular linear operators on is


    and the number of distinct -dimensional subspaces of is




    عدل سابقا من قبل Asmaa Mahmoud في الجمعة 25 يوليو 2008, 5:32 pm عدل 1 مرات (السبب : لتنسيق الموضوع)

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    Asmaa Mahmoud
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    m11 رد: vector space

    مُساهمة من طرف Asmaa Mahmoud في السبت 26 يوليو 2008, 12:08 pm

    thank's alot shady
    sorry but i have one qut.
    this topic in geometry or topology
    i think in top
    then vector space the same of the meaning of top. space?????????
    shady this properties remember me by function analysis right


      الوقت/التاريخ الآن هو السبت 15 ديسمبر 2018, 6:44 am