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!

An Example of a 2-Dimensional Subspace of C[0,1]

  1. Apr 16, 2014 #1

    sheldonrocks97

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Give an example of show that no such example exists.

    A two dimensional subspace of C[0,1]

    2. Relevant equations

    None that I know of.

    3. The attempt at a solution

    I know that C[0,1] is a set of continuous functions but I'm not sure where to go after that.
     
  2. jcsd
  3. Apr 16, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Define what 'two dimensional' means. That should be a clue.
     
  4. Apr 16, 2014 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Possibly a further clue: how would you find a two-dimensional subspace of ##\mathbb{R}^n##?
     
  5. Apr 16, 2014 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Polynomials are continuous functions, aren't they? It should be easy to determine the dimension of a subspace of polynomial functions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted