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: (a unit eigenvector)help!

  1. Dec 5, 2005 #1
    If A is a symmetric nxn mx of rank<=r>=1 and X is a unit eigenvector of A, with eigenvalue a not= 0, let B=A - aXX^T. Show that B is symmetric and that N(A) is a proper subspace of N(B). Conclude that rank B=<r-1.
    i could show X is in N(B) but not in N(A). Does anyone know how I can prove it in general? Then,I could prove N(A) is a proper subspace of N(B). Thanks!
  2. jcsd
  3. Dec 6, 2005 #2
    I figured it out already.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook