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We define the condition number of a nonsingular matrix on a subspace, and consider the problem of finding a subspace of given dimension that minimizes the condition number of a given matrix. We give a...
Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as cert...
Compensating changes between a subjects' training and testing session in Brain Computer Interfacing (BCI) is challenging but of great importance for a robust BCI operation. We show that such changes a...
Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most o...
We prove that the intrinsic square function and the intrinsic Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a family of weighted subspaces of Morrey spaces. The c...
Abstract: We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherenc...
We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).
We assume data sampled from a mixture of d-dimensional linear subspaces with outliers distributed symmetrically around the origin. We study the recovery of the global l0 subspace (i.e., with largest n...
Let H be a Hilbert space and let A be a simple symmetric operator in H with equal deficiency indices d := n±(A) < 1. We show that if, for all  in an open interval I  R, the dimension of defect subsp...
Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s0 and s1 such that the set s0 lies in a finite gap of the set s1.
Let T : X → X be a linear operator on a complex Banach space. Denote by (T ) and R(, T ) its spectrum and resolvent.
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals.We then deduce that for some classes of classical univariate orthogonal...
Let $(\tilde Q,g) $ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),\...
In this paper, we explore how to constructively manipulate quantum information on the controllable systems or subspaces. It is revealed that one can make full use of distinguished properties of Pauli ...
Using a recent result of Batson, Spielman and Srivastava, We ob-tain a tight estimate on the dimension of ℓn p , p an even integer, needed to almost isometrically contain all k-imensional subspa...

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