In this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore-Penrose inverse, the Drazin inverse and the numerical range of some reciprocal matrices are obtained. In particular, the relations between reciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP matrices are studied. To illustrate the results, some numerical examples are also given.

The Frobenius group was de, ned more than 120 years ago and has been the center of interest for researchers in the , eld of group theory. This group has two parts, complement and kernel. Proving that the kernel is a normal subgroup has been a challenging problem and several attempts have been done to prove it. In this paper we prove some character theory properties of , nite Frobenius groups and also give proofs of normality of the kernel in special cases.

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In this paper, we investigate the convergence of a sequence of minimizing trajectories in in nite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is de ned as a total cost over the in nite horizon.

The relations between the spectrum of the matrix Q+ Rand the spectra of matrices (g+δ) Q+(a+b) R-QR-RQ, QR-RQ, aRb-QRQ, aRQR-(QR) 2, and bR-QR have been given assuming that the matrix Q+R is diagonalizable, where Q, R are {g,δ}-quadratic matrix and f; g-quadratic matrix, respectively, of order n.

In this paper, some elementary operations on triangular fuzzy numbers (TFNs) are defined. We also define some operations on triangular fuzzy matrices (TFMs) such as trace and triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented. The concept of adjoints on TFM is discussed and some of their properties are. Some special types of TFMs (e.g. pure and fuzzy triangular, symmetric, pure and fuzzy skew-symmetric, singular, semi-singular, constant) are defined and a number of properties of these TFMs are presented.