Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...

We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that returns a difference-of-Cholesky representation of indefinite matrices. Heuristics that promote sparsity can be applied directly to this modification.

In this paper, we present a new speech perceptual hashing authentication algorithm based on wavelet packet decomposition (WPD) for speech content authentication. Firstly, a wavelet packet coefficients matrix of wavelet reconstruction is generated from an original speech signal after high frequency pre-processing followed by wavelet packet decomposition. Secondly, the wavelet packet coefficients...

Covering-based rough sets provide an efficient theory to deal with covering data which widely exist in practical applications. Boolean matrix decomposition has been widely applied to data mining and machine learning. In this paper, three types of existing covering approximation operators are represented by boolean matrices, and then they are used to decompose into boolean matrices. First, we de...

We establish necessary and sufficient conditions, in the language of bidiagonal decompositions, for a matrix V to be an eigenvector matrix of a totally positive matrix. Namely, this is the case if and only if V and V −T are lowerly totally positive. These conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of V and V −T . Using these decompo...

The sparse Cholesky factorization of some large matrices can require a two dimensional partitioning of the matrix. The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. The subblocks are stored as dense matrices so BLAS3 routines can be used. However, since we are dealing with sparse matrices some zeros may be stored in those dense blocks. The overhead i...

In this paper, the problem of splitting a given matrix into sparse and low-rank matrices is investigated. The problem is when and how we can exactly do this decomposition. This problem is ill-posed in general and we need to impose some (sufficient) conditions to be able to decompose a matrix into sparse and low-rank matrices. This conditions can be categorized into two general classes: (a) dete...

In this paper, a novel saliency theory based RR-IQA metric is introduced. As the human visual system is sensitive to the salient region, evaluating the image quality based on the salient region could increase the accuracy of the algorithm. In order to extract the salient regions, we use blob decomposition (BD) tool as a texture component descriptor. A new method for blob decomposition is propos...

This paper investigates the performance of multiple-input multiple-out (MIMO) wireless communication systems in a multiuser environment. The user information is defined by a data matrix generated by the observed input-output data of the system, from which subspace identification method is developed using LQ-decomposition of the matrix. The LQ-decomposition is basically used to solve for the use...

magnesium hydroxide nanostructures as an effective flame retardant were synthesized by a facile and rapid microwave reaction. the effect of different surfactants such as cationic, anionic and polymeric on the morphology of magnesium hydroxide nanostructures was investigated. nanostructures were characterized by x-ray diffraction (xrd), scanning electron microscopy (sem) and fourier transform in...