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Given $n times n$ real symmetric matrices $A_1, dots, A_m$, the following {it spectral minimax} property holds: $$min_{X in mathbf{Delta}_n} max_{y in S_m} sum_{i=1}^m y_iA_i bullet X=max_{y in S_m} min_{X in mathbf{Delta}_n} sum_{i=1}^m y_iA_i bullet X,$$ where $S_m$ is the simplex and $mathbf{Delta}_n$ the spectraplex. For diagonal $A_i$s this reduces to the classic minimax.
Is is shown here that the simple test of quantumness for a single system of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the quantum system
The concept of a classical player, corresponding to a classical random variable, is extended to include quantum random variables in the form of self adjoint operators on infinite dimensional Hilbert space. A quantum version of Von Neumanns Minimax th
We prove that a fractional perfect matching in a non-bipartite graph can be written, in polynomial time, as a convex combination of perfect matchings. This extends the Birkhoff-von Neumann Theorem from bipartite to non-bipartite graphs. The algorit
A unital ring is called clean (resp. strongly clean) if every element can be written as the sum of an invertible element and an idempotent (resp. an invertible element and an idempotent that commutes). T.Y. Lam proposed a question: which von Neumann
We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse problems.