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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

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    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
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