We propose an extension of the Grevile’s partitioning method for computing the Moore-Penrose inverse of two-variable rational and polynomial complex matrices. Also we developed corresponding effective algorithm, applicable in the case when there are only few degrees in A(s1, s2) corresponding to nonzero coefficient matrices. These algorithms are implemented using symbolic and functional possibi...

The method is proposed for reduction of hardware amount in logic circuit of Moore finite state machine. The method is oriented on CPLD technology. It is based on representation of the next state code as a concatenation of codes for class of pseudoequivalent states and collection of microoperations. Such an approach allows elimination of dependence among states and microoperations. As a result, ...

The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James–Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space. An abelian group A determines the Moore space M(A) = M(A, 2) which up to homotopy equiv...

In this paper we study the class of square matrices A such that AA − AA is nonsingular, where A stands for the Moore–Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA−AA is nonsingular if and only if R(A) ⊕ R(A) = Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A) = R(A).