We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...

Matrix nearness problems have been the focus of much research in linear algebra; see, e.g., [8,9,19,32]. In particular, characterizations of the algebraic variety of normal matrices and distance measures to this variety have received considerable attention; see [10,11,13,14,16,17,23,25–27]. Normal matrices are of interest because their eigenvalues are optimally conditioned and their singular va...

We report a novel rotary piezoelectric motor using bending transducers in this work. Three transducers are used to drive a disk-shaped rotor together by the elliptical movements of their driving tips; these motions are produced by the hybrid of two first bending vibration modes. The proposed piezoelectric transducer has a simple structure as it only contains an aluminum alloy beam and four piec...

In the context of Krylov methods for solving systems of linear equations, expressions and bounds are derived for the norm of the minimal residual, like the one produced by GMRES or MINRES. It is shown that the minimal residual norm is large as long as the Krylov basis is well-conditioned. In the context of non-normal matrices, examples are given where the minimal residual norm is a function of ...

in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

in this article we study steensen method to solve nonlinear matrix equation x+a^t x^(-1) a=q, when a is a normal matrix. we establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.