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

Please help me prove this (desperate)

  1. Oct 25, 2004 #1
    For an n*n matrix C=(cij) over R or C, we define v(C)=Max|cij|

    a.Show that if A is invertible, then B is invertible if v(A-B) is sufficiently small.

    b. Show that for any, not necessarily invertible, n*n matix A, there is a sequence Ak of invertible matrices with v(A - Ak) -> 0 .
  2. jcsd
  3. Oct 25, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    If v(X)<e, it appears that a result along the lines of det(XY) < e^n * det(Y) is true. If so, you can use this for part a.

    part b looks a little harder.

    does this v define a (metric) topology on the nxn matrices?
  4. Oct 25, 2004 #3
    thanks for the hint on part a, the v in part b is the same as in part a
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Please help me prove this (desperate)
  1. Please help me. (Replies: 1)

  2. Please help me (Replies: 2)