The fault diagnosis precision for rolling bearings under variable conditions has always been unsatisfactory. For solving this problem, a feature extraction method combing the Hilbert-Huang transform with singular value decomposition was proposed in this paper. The method includes three steps. Firstly, instantaneous amplitude matrices were obtained by Hilbert-Huang transform from rolling bearing...

We study linear spaces of n × n matrices in which every matrix is singular. Examples are given to illustrate that a characterization of such subspaces would solve various open problems in combinatorics and in computational algebra. Several important special cases of the problem are solved, although often in disguise. 1. The problem Let A be a linear subspace of the space IR n×n of real n × n ma...

We propose and analyze additive preprocessing for computing the vectors in and bases for the null spaces of matrices. Instead of singular linear systems we solve nonsingular ones that preserve the conditioning properties and the structure of the input matrices. For ill conditioned input we can extend our preprocessing further, to decrease the problem size. Our approach is readily extended to th...

A preorder on the line-of-sight (LOS) matrices in coherent multipleinput multiple-output (MIMO) Ricean fading channels is introduced. It is demonstrated that under this preorder, the information rate corresponding to zero-mean multivariate circularly symmetric Gaussian inputs of arbitrary covariance matrices is monotonic in the LOS matrix. This result implies the monotonicity of the information...

Given a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A+∆A+ μ(E +∆E), one approach for general singular pencils and another one such that A+∆A and E + ∆E have a common left/right...

We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = UkΣkV T k , where Σk is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1 ≥ σ2 · · ...

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse...

In this paper we derive a new algorithm for constructing a unitary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and right transformations on the individual matrices and amounts to computing the generalized singular value decomposition of the sequence. The proposed algorithm is related to the classical Golub–Kahan proce...

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey ([12]) and Rao ([3]) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems (cf. [3], Theorems 5 and 7 and [4]). We a...

Hankel matrices are an important family of matrices that play a fundamental role in diverse fields of study, such as computer science, engineering, mathematics and statistics. In this paper, we study the behavior of the singular values of the Hankel matrix by changing its dimension. In addition, as an application, we use the obtained results for choosing the optimal values of the parameters of ...