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Homework Help: Invertible Complex Matrices

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Does there exist a matrix A such that the entire family A + cI is invertible for all complex numbers c?

    2. Relevant equations
    A matrix is invertible if det(A) != 0

    I really have no clue where to go with this problem. Any hints or suggestions would be greatly helpful, even if you can't give an answer to the problem.
  2. jcsd
  3. Apr 8, 2009 #2
    What kind of function is f(c)=det(A+cI)?
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