It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive sheaves of any rank; on the contrary fo...

The generalized inverse has numerous important applications in aspects of the theoretic research matrices and statistics. One core problems is finding necessary sufficient conditions for reverse (or forward) order laws matrix products. In this paper, by using extremal ranks Schur complement, some are given forward law A1{1,2}A2{1,2}…An{1,2}⊆(A1A2…An){1,2}.

and Applied Analysis 3 to a class of complex matrix equations with conjugate and transpose of the unknowns. Jonsson and Kågström 24, 25 proposed recursive block algorithms for solving the coupled Sylvester matrix equations and the generalized Sylvester and Lyapunov Matrix equations. Very recently, Huang et al. 26 presented a finite iterative algorithms for the one-sided and generalized coupled ...

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.