Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Nullity-Rank question

  1. Oct 17, 2012 #1
    Just a quick question I've been giving some thought to today. Suppose A is an mxn matrix with column vectors such that only one of them is a scalar transformation of another. What can we say about the relationship of m and n?
     
  2. jcsd
  3. Oct 17, 2012 #2
    No thoughts?
     
  4. Oct 17, 2012 #3

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    what is a "scalar transformation"? if it means scalar multiple, then i don't see right off how to say anything. if it means linear combination, in the sense that there are n-1 independent columns, then it say the column rank is n-1. since then the row rank must also be n-1, we know there are at least n-1 rows, so m ≥ n-1.

    your problem in receiving no answers is your unclear statement of the question.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Nullity-Rank question
  1. Rank question (Replies: 4)

  2. Rank question (Replies: 2)

Loading...