The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimensi...

In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...

A Gram-Schmidt type algorithm is given for finite d-dimensional reflexive forms over division rings. The algorithm uses d/3 + O(d) ring operations. Next, that algorithm is adapted in two new directions. First a sequential algorithm is given whose complexity matches the complexity of matrix multiplication. Second, a parallel NC algorithm is given with similar complexity.

Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetr...

Linear matrix equations play an important role in many areas, such as control theory, system theory, stability theory and some other fields of pure and applied mathematics. In the present paper, we consider the generalized coupled Sylvestertranspose and conjugate matrix equations Tν(X) = Fν , ν = 1, 2, . . . , N, where X = (X1, X2, . . . , Xp) is a group of unknown matrices and for ν = 1, 2, . ...