Speaker: Alexander Guterman
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Title: On idempotent matrices
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Abstract: Idempotent matrices play a significant role while dealing
with different questions in matrix theory and its applications.  It is
easy to see that over a field any idempotent matrix is similar to a
diagonal matrix with 0 and 1 on the main diagonal. Over a semiring the
situation is quite different.  For example, the matrix $J$ of all ones
is idempotent over Boolean semiring.  The problem of the
characterization of idempotent matrices over semirings was posed by
Flor in 1969, who solved the problem for matrices over the semiring of
non-negative integers. In this talk we solve this problem for matrices
over the binary Boolean semiring.

Some related results and applications will be presented. In
particular, we construct minimal idempotent envelope of a given matrix
and describe all matrices that are majorized by a given idempotent
matrix with respect to a minus order.  Also we compare the structure
of idempotents over semirings with the structure of idempotents over
fields and rings.
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