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: Inverse of outer-product

  1. Jul 8, 2010 #1
    Hi All,

    This is not a homework or coursework question. Yet I have a curiosity.

    If a matrix [tex]A[/tex] is an outer-product of a vector [tex]v[/tex] as : [tex]A = v v^{\top}[/tex]

    Then can [tex]A^{-1}[/tex], inverse of [tex]A[/tex], be also expressed as an outer-product of some other vector?

    Please point me how to approach the question, how to find the answer or how to say it is possible or not.

  2. jcsd
  3. Jul 8, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If A is 0x0 or 1x1, inverting it is easy. Otherwise...

    Exercise: If v is nonzero, prove that A has rank 1.

    You can do better:

    Exercise: A matrix has rank 1 if and only if it is the outer product of two nonzero vectors.
  4. Jul 8, 2010 #3
    oops!! Thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Inverse outer product Date
Inverse trig functions Feb 16, 2018
Inverses in Z/mZ* Jan 31, 2018
Inverse Z transform problem Nov 20, 2017
The adjoint of the inverse Oct 22, 2017
Nonmeasurable Set with Finite Outer Measure Sep 24, 2017