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!

Homework Help: Dimension of a matrix vectorspace

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F .

    3. The attempt at a solution

    The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be n*m? For the basis (it has m*n elements), would it simply be zero matrices with a 1 in the "ij" entry, starting at 1,1 and ending at n,m?
    I feel like the question is just too easy, which is leading me to doubt my answer...
     
  2. jcsd
  3. Jan 13, 2012 #2
    That seems correct.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...