Linear Algebra, Operator Theory of bounded operators.
are focused on several themes. Among them are:
Representation of a matrix (or a bounded operator) by a linear
combination (+1,"+"or "-" 1, integer, positive, real, complex coefficients)
of idempotents or orthoprojections.
Representation of a matrix as a product of unitary matrices with a fixed spectrum.
Applications of a sum and a product of projections in Numerical Analysis, Knots Theory,
Functional Analysis and so on.
Applications of the inverse eigenvalue problem: finding the possible
spectrum of G=A+B+C+..., where A, B, C... are projections.
Finding siutable initial spectra data for solvability of inverse spectral problems for weighted
grphs or(and) sign patterns.
Describing complete sets of unitary invariants of a matrix. Invariant Theory and Representations.
17th INTERNATIONAL CONFERENCE ON DOMAIN DECOMPOSITION METHODS,
St. Wolfgang/Strobl, Austria, July, 3-7, 2006,
Here is the DVI file of the slides I used in
my talk there.