arXiv subjects
Publications and source records attributed to T. Kurmayya.
A number of the form $a_s+a_d \epsilon$, where $a_s, a_d \in\mathbb{C}^{n \times n}$ and $\epsilon$ is an infinitesimal unit satisfying $\epsilon^2=0$, is called a dual number. A matrix with dual number entries is known as dual matrix. The objective of this article is to derive a polar decomposition of dual matrices and to study the existence and uniqueness conditions. To illustrate these results, some examples are constructed.
In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These comparison results are useful to analyse the rate of convergence of the iterative methods (formulated from the double splittings) for solving rectangular linear system Ax = b.
In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed convex cones.
In this paper we derive necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators between real Hilbert spaces. These conditions include statements on acuteness of certain closed convex cones. The main result generalizes the existing result for bounded operators [11, Theorem 3.6].