We show that the maximum moments of the sum of independent positive semidefinite random matrices with given norm upper bounds and norms of expectations is attained when all the random matrices are the multiplications of certain random variables and the identity matrix....
摘要: The purpose of this paper is to present some inequalities on majorization, trace, eigenvalue and singular for sum of complex, Hermitian and positive semidefinite matrices.关键词:eigenvalues singular values frobenius norm inequality 会议名称: Fifth International Conference on Information & Computing...
In practice, K is often the nonnegative orthant, the second-order cone (or quadratic cone, or Lorentz cone) or the cone of positive semidefinite matrices (semidefinite pro- gramming or SDP cone for short), as well as direct products of these cones. For instance, the basic SDP feasibility...
This topic is of interest in connection with the Lieb–Seiringer formulation of the Bessis–Moussa–Villani conjecture, which asks whether Tr( S m , k ( A , B ))≥0 holds for all positive semidefinite matrices A and B . These results eliminate the possibility of using "descent + sum-...
摘要: The sum of the k×k principal minors of the matrix(A+tB)m is a polynomial with positive coefficients(in t) in the cases of k=n(any m) and m3(any k,h),when one of matrices A and B is definite and the other is semidefinite....
These chordal SOS decomposition theorems for polynomial matrices extend a classical chordal decomposition result for constant (i.e., independent of x) positive semidefinite (PSD) sparse matrices [1]. The latter allows for significant computational gains when applied to large-scale sparse SDPs [45, ...
Finally, the dual of the lower prevision problem (18) is then given by the convex SemiDefinite Programming (SDP) problem:(26)infy∈Rsn(2d)L(h),s.t.L(g)≥0,L(1)=1,Mn,d(y)≥0. 5.2. Non-SOS positive polynomials What does it mean for our theory of bounded rationality that ...
Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables...
Some inequalities for sum and product of positive semidefinite matrices[J].Linear Algebra and its Applications,1999.39-49.doi:10.1016/S0024-3795(99)00013-0.Wang B Y,Xi B Y,Zhang F Z. Some inequalities for sum and products of positive semidefinite matrices[J].Linear Algebra and its ...
Operations Research Letters: A Journal of the Operations Research Society of AmericaXia Y,Wang L F,Wang S.Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices:approximation and applications[J].Operations Research Letters,2017.DOI:10.1016/j.orl.2017.11.010...