This paper describes a minimax state estimation approach for linear differential-algebraic equations (DAEs) with uncertain parameters. The approach addresses continuous-time DAEs with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation function. Main result is a Generalized ...

Low-rank matrix approximation is an integral component of tools such as principal component analysis (PCA), as well as is an important instrument used in applications like web search, text mining and computer vision, e.g., face recognition. Recently, randomized algorithms were proposed to effectively construct low rank approximations of large matrices. In this paper, we show how matrices from e...

In this paper, {α, k}-group periodic matrices are introduced and analyzed. Using different approach (as {1}-inverses, Moore-Penrose inverse, elementary matrices, left and right inverses and singular value decomposition) we characterize this kind of matrices. Some results presented are an extension of those known about group inverse and group periodic matrices. Key–Words:Generalized inverse, gro...

These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane as the dimension n tends to infinity. This phenomenon is the non-Hermitian counterpart of the semi circular limit for Wigner random Hermitian matrices, ...

For fixed l,m ≥ 1, let X n ,X n , . . . ,X n be independent random n × n matrices with independent entries, let F n := X n (X n )−1 · · · (X n )−1, and let F (1) n , . . . ,F (m) n be independent random matrices of the same form as F (0) n . We investigate the limiting spectral distributions of the matrices F (0) n and F (1) n +. . .+F (m) n as n→∞. Our main result shows that the sum F n +. . ....

In this article, we establish a limiting distribution for eigenvalues of class autocovariance matrices. The same has been found in the literature regularized version these original nonregularized matrices are noninvertible, thus introducing supplementary difficulties study their through Girko’s Hermitization scheme. key result paper is new polynomial lower bound specific family least singular v...

New perturbation theorems are proved for simultaneous bases of singular subspaces of real matrices. These results improve the absolute bounds previously obtained in [6] for general (complex) matrices. Unlike previous results, which are valid only for the Frobenius norm, the new bounds, as well as those in [6] for complex matrices, are extended to any unitarily invariant matrix norm. The bounds ...

Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for ...

The Capon-MVDR (Minimum Variance Distortionless Response) method of frequency-wavenumber spectral estimation requires an invertible spatial covariance estimate. Increasingly, however, one must deal with a singular covariance matrix. The ubiquity of inexpensive sensors implies that the dimension of the covariance matrix is ever-increasing, but coherence times have not changed, so the number of v...