1. Not finding help here? Sign up for a free 30min 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!

If a matrix A is injective then AAt is invertible

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data
    If a matrix, A (nxm) is monic (or epic) then is [tex]A^tA (or AA^t)[/tex] is invertible?


    2. Relevant equations
    T is monic if for any matrices B,C: BT = BT => B=C.
    S is invertible if there exists U s.t. US = SU = [tex]I_n[/tex]



    3. The attempt at a solution
    Since A is monic it must preserve n; i.e. assume n < m, so that A has n independent rows (is that allowed), and we view A as an function of natural numbers, [tex] n \stackrel{A}{\rightarrow} m[/tex]. Then can we say AB where B is m * k, means that AB has n indepenent rows as well?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: If a matrix A is injective then AAt is invertible
  1. Matrix Question (Replies: 0)

  2. Vandermonde matrix (Replies: 0)

  3. Rotation Matrix (Replies: 0)

Loading...