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: Howto define the Column space of nxn matrix

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data

    I thought that if you have a square matrix then the column space is the set of all linear independent vectors which can be written as a linear combinations of the others? Which inturn is the same as range of the Matrix?
    Am I wrong?
  2. jcsd
  3. Feb 8, 2010 #2
    The column space of a matrix is the set of all possible linear combinations of its column vectors.
    It is the same as the range for the corresponding transformation matrix.
  4. Feb 8, 2010 #3
    and thats the same as the range of the matrix?
  5. Feb 8, 2010 #4
    Yes, it is the same as the range of the matrix (for the corresponding transformation).
  6. Feb 8, 2010 #5
    It little follow-up question the same n x n matrix B is a 6 x 6 then then following how do I show if the matrix equation Bx = c has a solution for all [tex]c \in \mathbb{R}^6[/tex] is that if all the columns in B are linear independent and thusly spans the whole of [tex] \mathbb{R}^6[/tex] and then claim is true? and if they don't the claim is false for the matrix B?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook