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Recently, O. Taussky raised the
following question. Given a nonnegative n×n matrix A = (ai,j), let ΩA be the set of
all n × n complex matrices defined by
Then, defining the spectrum S(M) of an arbitrary set M of n × n matrices B
as
what can be said in particular about S(ΩA)? It is not difficult to see that S(ΩA)
consists of possibly one disk and a series of annular regions concentric about the
origin, but our main result is a precise characterization of S(ΩA) in terms of the
minimal Gerschgorin sets for A.
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