| Abstract |
We consider pairs of linear mappings
(A,B) of the form
VA→←1B1W
in which V and W are
finite dimensional unitary or Euclidean spaces over C
or R, respectively. Let (A,B) be
transformed to VA′→←1B′1W
by bijections
φ1:V→V′ and φ2:W→W′. We say
that (A,B) and (A′,B′) are linearly
equivalent if φ1 and φ2 are linear bijections
and topologically equivalent if φ1 and φ2
are homeomorphisms. We prove that (A,B) and (A′,B′) are topologically equivalent if and only if their
regular parts are topologically equivalent and their singular
parts are linearly
equivalent. |
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