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!

Lin. Alg. Invertility

  1. May 15, 2009 #1
    To find out if 4 in an eigenvalue of A, decide if A-4I is invertible...

    So, if A-4I is invertible, then its cols are lin ind by IMT, and also there is only the trivial solution to A-4I=0, so thus 4 is not an eigenvalue of A

    ?
     
  2. jcsd
  3. May 15, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    ???? The definition of "eigenvalue" is that [itex]\lambda[/itex] is an eigenvalue if and only if [itex]Av= \lambda v[/itex] has non-trivial solutions. That is the same as saying that [itex]Av- \lambda v= (A- \lambda I)v= 0[/itex] has non-trivial solutions. Since v=0 is obviously a solution, saying it has non-trivial solutions means it does NOT have a "unique" solution. If the matrix M has an inverse, then the equation Mv= u has the unique solution [math]v= M^{-1}u[/math].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lin. Alg. Invertility
  1. Lin Alg proof problem (Replies: 1)

  2. In^-1=In Lin alg (Replies: 4)

Loading...