1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear subspace of R^n

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Is the set of all vectors in R^n whose components form an arithmetic progression a linear subspace of R^n?

    2. Relevant equations


    3. The attempt at a solution

    I basically need one thing verified: would (0,0,0,...,0) be considered an arithmetic progression. The definition says that an arithmetic progression is one where the difference between any two consecutive members of the sequence is constant. Since 0-0=0, it would seem like it is an arithmetic sequence, however, is there a condition that the difference must be non-zero? If not, then (1,1,...,1), (2,2,...,2), etc. would all be arithmetic progressions, and that doesn't seem right to me.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 8, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    No, I don't think there's any condition on an arithmetic sequence saying the difference can't be zero.
  4. Nov 8, 2009 #3
    alright, so in that case it is a linear subspace since it meets the three requirements to be a linear subspace. Thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear subspace of R^n
  1. Subspace of R^n (Replies: 1)