An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

Fast algorithms based on the matrix sign function are developed to estimate the signal and noise subspaces of the sample correlation matrices. These subspaces are then utilized to develop high resolution methods such as MUSIC and ESPRIT for sinusoidal frequency and direction of arrival (DOA) problems. The main feature of these algorithms is that they generate subspaces that are parameterized by...

In this paper, we study the lower semilattice of NP-subspaces of both the standard polynomial time representation and the tally polynomial time representation of a countably infinite dimensional vector space V, over a finite field F. We show that for both the standard and tally representation of V, , there exists polynomial time subspaces U and FV such that U + V is not recursive. We also study...

Codes in the Grassmannian space have found recently application in network coding. Representation of kdimensional subspaces of Fq has generally an essential role in solving coding problems in the Grassmannian, and in particular in encoding subspaces of the Grassmannian. Different representations of subspaces in the Grassmannian are presented. We use two of these representations for enumerative ...

Large scale eigenvalue computation is about approximating certain invariant subspaces associated with the interested part of the spectrum, and the interested eigenvalues are then extracted from projecting the problem by approximate invariant subspaces into a much smaller eigenvalue problem. In the case of the linear response eigenvalue problem (aka the random phase eigenvalue problem), it is th...

Given two chains of subspaces in C, we study the set of unitary matrices that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U− In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, we give formula for the minimum value ‖U − In‖, and describe the set of all the unitary matrices in the set attaining the minimum...

In this short note we report on invariant subspaces in Simpira in the case of four registers. In particular, we show that the whole input space (respectively output space) can be partitioned into invariant cosets of dimension 56 over F 28 . These invariant subspaces are found by exploiting the non-invariant subspace properties of AES together with the particular choice of Feistel configuration....

Robust clustering of data into overlapping linear subspaces is a common problem. Here we consider one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using an EM procedure, where the E-step calculates posterior probabilities ...

Robust clustering of data into linear subspaces is a common problem. Here we treat clustering into one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using a modified k-means procedure, where line orientations and distances ...

Most applications of quantum information require many qubits, which means that they must be described using state spaces of very high dimension. The geometry of such spaces is invariably simple but often surprising. Subspaces, in particular, can be interpreted as quantum error correcting codes and, when the dimension is high enough, random subspaces form remarkably good codes. This is because i...