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Loop symmetric functions and factorizing matrix polynomials
Loop symmetric functions factorizing matrix polynomials
2011/1/18
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surface...
Strict Positivstellens\" atze for matrix polynomials with scalar constraints
matrix polynomials scalar constraints
2010/11/24
We extend Krivine's strict positivstellensatz for usual (real multivariate) polynomials to symmetric matrix polynomials with scalar constraints. The proof is an elementary computation with Schur compl...
Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States
Deciding Unitary Equivalence Matrix Polynomials Sets of Bipartite Quantum States
2010/10/29
In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebr...