Any Hilbert space of composite dimension can be decomposed into a tensor product spaces lower dimensions. Such factorization makes it possible to decompose quantum system subsystems. Using modification mechanics in which the continuous unitary group is replaced with permutation representation finite group, we suggest model for constructive study decompositions closed To investigate behavior sys...

We prove that any symplectic matrix can be factored into no more than 5 unit triangular matrices, moreover, is the optimal number. This result improves existing factorization of matrices which gives proof 9 factors. also show corresponding improved conclusions for structured subsets matrices. further provides an unconstrained optimization method on 2d-by-2d real group (a 2d2+d-dimensional Lie g...

For about ten years now, Bo K̊agström’s Group in Umea, Sweden, Jerzy Waśniewski’s Team at Danish Technical University in Lyngby, Denmark, and I at IBM Research in Yorktown Heights have been applying recursion and New Data Structures (NDS) to increase the performance of Dense Linear Algebra (DLA) factorization algorithms. Later, John Gunnels, and later still, Jim Sexton, both now at IBM Research ...

We find a natural compatible condition between the Rota-Baxter operator and Turaev's (Hopf) group-(co)algebras, which leads to concept of group-(co)algebra. Two characterizations group-algebras (abbr. T-algebras) are obtained: one by Atkinson factorization other T-quasi-idempotent elements. The relations among some related group algebraic structures (such as (tri)dendriform T-algebras, Zinbiel ...

Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schrödinger hierarchy is picked out for illustration of the classical case. This system is formulated as a dynamical system on a Lie group of Laurent series with factorization st...

Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...