Related papers: Embeddable Markov Matrices
We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of…
We work in the space of $m$-by-$n$ real matrices with the Frobenius inner product. Consider the following Problem: Given an m-by-n real matrix A and a positive integer k, find the m-by-n matrix with rank k that is closest to A. I discuss a…
Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We…
We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem.…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential…
The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation…
We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic…
We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak in the case of quadratic map. We…
Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…
Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, raise in the quantum computation, bin-packing and matrix analysis. We find the…
We give an almost-complete description of orthogonal matrices $M$ of order $n$ that "rotate a non-negligible fraction of the Boolean hypercube $C_n=\{-1,1\}^n$ onto itself," in the sense that $$P_{x\in C_n}(Mx\in C_n) \ge n^{-C},\mbox{ for…
We note that building a magnetic Laplacian from the Markov transition matrix, rather than the graph adjacency matrix, yields several benefits for the magnetic eigenmaps algorithm. The two largest benefits are that the embedding becomes more…
Recently two approximate Newton methods were proposed for the optimisation of Markov Decision Processes. While these methods were shown to have desirable properties, such as a guarantee that the preconditioner is negative-semidefinite when…
We show that the quantum $R$ matrix for symmetric tensor representations of $U_q(A^{(1)}_n)$ satisfies the sum rule required for its stochastic interpretation under a suitable gauge. Its matrix elements at a special point of the spectral…
We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\geq N $ single-particle orbitals are sought iteratively so that the projection of the given wave…