Motivated by the definition of P†-matrix ([9]), another generalization of a P -matrix for square singular matrices called PD-matrix is proposed first. Then the uniqueness of solution of Linear Complementarity Problems for square singular matrices is proved using PD-matrices. Finally some results which are true for P -matrices are extended to PD-matrices.

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...

We study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the `q-quasinorm with 0 < q ≤ 1. Mainly we study the decay of the lower and upper tail probabilities of the largest q-singular value s 1 , when the number of rows of the matrices becomes very large. Furthermore, we also give probabilistic estimates for the smallest q-singular value of pre-Gaussian ra...

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 ...

Abstract. We study the q-singular values of random matrices with preGaussian entries defined in terms of the q-quasinorm with 0 < q ≤ 1. In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value s 1 , when the number of rows of the matrices becomes very large. Based on the results in probabilistic estimates on the largest q-singular va...

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. Hmatrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance prop...