Results 1 to 3 of 3

Math Help - integer modulo 4 vectors

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    190
    Thanks
    3

    integer modulo 4 vectors

    Hi;

    is there anything wrong in saying that if u is a vector over Z_4 then for all a,b \in Z_4\; au+bv=u+u+...+u+v+v+...+v=(a+b)v
    so that the distributive property holds for vectors over Z_4.

    Also if

    c_1v_1+c_2v_2+...+c_kv_k=a_1v_1+a_2v_2+...+a_kv_k

    then by the inverse property of groups and the above distributive property

    (c_1-a_1)v_1+(c_2-a_2)v_2+...+(c_k-a_k)v_k=0

    where 0 is the zero vector.


    Is there anything wrong with my post at all no matter how trivial? thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Krahl View Post
    Hi;

    is there anything wrong in saying that if u is a vector over Z_4 then for all a,b \in Z_4\; au+bv=u+u+...+u+v+v+...+v=(a+b)v
    so that the distributive property holds for vectors over Z_4.

    Also if

    c_1v_1+c_2v_2+...+c_kv_k=a_1v_1+a_2v_2+...+a_kv_k

    then by the inverse property of groups and the above distributive property

    (c_1-a_1)v_1+(c_2-a_2)v_2+...+(c_k-a_k)v_k=0

    where 0 is the zero vector.


    Is there anything wrong with my post at all no matter how trivial? thanks
    What exactly are you asking? If it's a vector field?

    Well...maybe you mean field? No, it has non-trivial zero divisors (2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2009
    Posts
    190
    Thanks
    3
    no, i know Z_4^n isn't a field, i was just wondering whether any of my ascertions were true. it doesn't form a vector space but it does form a structure (with different definitions of linear independence, v_1,v_2,...,v_k are linearly independent if c_1v_1+...+c_kv_k=0 \Longrightarrow c_iv_i=0 \forall i), and i wanted to know whether i could say the distributive property holds in the above sense. Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 13
    Last Post: August 3rd 2010, 03:16 AM
  2. Integer roots of integer polynomials
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 3rd 2009, 12:39 PM
  3. Modulo of squares = modulo of roots
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: December 1st 2009, 09:04 AM
  4. Raise integer to positive integer power
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 21st 2009, 12:20 PM
  5. Inverse of an integer modulo m
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: March 4th 2008, 01:23 PM

Search Tags


/mathhelpforum @mathhelpforum