A deep factorization of the orthogonal projection matrix onto a subspace is obtained. The LQ decomposition used. For construction an Q method successive rank reduction applied.

In this paper, we present a method to estimate the signal subspace at all frequencies in given band, which is computed from usual set of frequency-bin sample covariance matrices wideband estimation. Fundamentally, exploits similarity between any two near-by produce an improved along band. Its key idea consists modeling by means projection matrix function approximated polynomial. The provides im...

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outsi...

In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation ...

In this paper, we propose a robust motion segmentation method based on the matrix factorization and subspace separation. We, first, mathematically prove that the shape interaction matrix can be derived using QR decomposition rather than Singular Value Decomposition(SVD). Using shape interaction matrix, we solve the motion segmentation problem using spectral graph clustering technique. We exploi...

This paper describes two methods for computing the invariant subspace of a matrix. The rst method involves using transformations to interchange the eigenvalues. The matrix is assumed to be in Schur form and transformations are applied to interchange neighboring blocks. The blocks can be either one by one or two by two. The second method involves the construction of an invariant subspace by a di...

We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension (S + 1) 2 . This subspace is des...

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive high-dimensional problems. Iterative random sparsification allow the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated sampling and averaging. We present general approach to extending such multiple demonstrate its performance several benchmark problems in quantum chemistry.

Introduction: In the recent decade, there have been significant efforts in developing multiuser detection technologies to alleviate the effect of multiple access interference (MAI) in codedivision multiple-access (CDMA) systems. Blind multiuser detection is of special interest for MAI mitigation in CDMA systems since it is impractical to assume perfect knowledge of parameters such as spreading ...