A generalized Stiefel manifold is the of orthonormal frames in a vector space with nondegenerated bilinear or hermitian form. In this article, Isometry group manifolds are computed at least up to connected components an explicit This done by considering natural nonassociative algebra m associated affine structure manifold, computing explicitly automorphism Aut(

A new class of measurement operators, coined hierarchical and prove results guaranteeing the efficient, stable robust recovery hierarchically structured signals from such measurements. We derive bounds on their restricted isometry properties based constants constituent matrices, generalizing extending prior work Kronecker-product As an exemplary application, we apply theory to two communication...

We point out that if spatial information is encoded through linear operators Xi, or ‘infinite-dimensional matrices’ with an involution X∗ i = Xi then these Xi can only describe either continuous, discrete or certain ”fuzzy” space-time structures. We argue that the fuzzy space structure may be relevant at the Planck scale. The possibility of this fuzzy space-time structure is related to subtle f...

Compressive Sampling (CS) describes a method for reconstructing high-dimensional sparse signals from a small number of linear measurements. Fundamental to the success of CS is the existence of special measurement matrices which satisfy the so-called Restricted Isometry Property (RIP). In essence, a matrix satisfying RIP is such that the lengths of all sufficiently sparse vectors are approximate...

The study of linear algebra has become more and more popular in the last few decades. People are attracted to this subject because of its beauty and its connections with many other pure and applied areas. In theoretical development of the subject as well as in many applications, one often needs to measure the “length” of vectors. For this purpose, norm functions are considered on a vector space...

Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrary different. Particularly, there exist codes with the fu...

A map T: Ej —► E2 (E|, E2 Banach spaces) is an e-isometry if III T(X) T(Y)\\ \\X Y\\ I < e whenever X, Ye Ex. The problem of uniformly approximating such maps by isometries was first raised by Hyers and Ulam in 1945 and subsequently studied for special infinite dimensional Banach spaces. This question is here broached for the class of finite dimensional Banach spaces. The only positive homogene...

Let X be a proper CAT(0)-space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is non-elementary and contains a rank-one element then its second bounded cohomology group with coefficients in the regular representation is non-trivial. As a consequence, up to passing to an open subgroup of finite index, either G is a compact extension of a totally disconnected ...

The restricted isometry condition. The proof that the Restricted Isometry Condition is sufficient for sparse recovery using convex programming is due to Candes and Tao [2]. A simpler proof, also due to Candes and Tao, is in [4]. Applications of restricted isometries to vector quantization and democratic coding are found in [10], and applications to computing the condition number of random matri...