Related papers: Localization of complementarity eigenvalues
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
We focus on the non-locality concerning local copying and local discrimination, especially for a set of orthogonal maximally entangled states in prime dimensional systems, as a study of non-locality of a set of states. As a result, for such…
A group homomorphism eta:H-->G is called a localization of H if every homomorphism phi:H-->G can be `extended uniquely' to a homomorphism Phi:G-->G in the sense that Phi eta=phi. Libman showed that a localization of a finite group need not…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell's theorem, and can be used to certify…
We prove localization with high probability on sets of size of order $N/\log N$ for the eigenvectors of non-Hermitian finitely banded $N\times N$ Toeplitz matrices $P_N$ subject to small random perturbations, in a very general setting. As…
Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…
The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through…
A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an…
Let K be a (commutative) field with characteristic not 2, and V be a linear subspace of n by n matrices that have at most two eigenvalues in K (respectively, at most one non-zero eigenvalue in K). We prove that the dimension of V is less…
Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high probability every eigenvector is delocalized, meaning any…
In this paper we give a first study of perfect copositive $n \times n$ matrices. They can be used to find rational certificates for completely positive matrices. We describe similarities and differences to classical perfect, positive…
We compute the local cohomology modules H_Y^(X,O_X) in the case when X is the complex vector space of n x n symmetric, respectively skew-symmetric matrices, and Y is the closure of the GL-orbit consisting of matrices of any fixed rank, for…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
B. Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of stable quasimaps and stable LG-quasimaps by studying localized Chern characters for 2-periodic complexes. In this paper, we study…
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…
For quantum Hamiltonian reductions in arbitrary characteristics, it is known that derived localization holds if and only if the algebra of global sections has finite global dimension. In this paper we provide an alternative characterization…