The rank subtractivity partial ordering is defined on Cn×n (n ≥ 2) by A ≤− B⇔ rank(B−A) = rankB− rankA, and the star partial ordering by A ≤∗ B⇔ A∗A = A∗B ∧ AA∗ = BA∗. If A and B are normal, we characterize A ≤− B. We also show that then A ≤− B ∧ AB = BA⇔ A ≤∗ B⇔ A ≤− B ∧ A ≤− B. Finally, we remark that some of our results follow from well-known results on EP matrices.

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its higher rank numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that ...

Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.

Functional links between bone remodeling and the immune system in chronic inflammatory arthritis are mediated, in part, by the ligand of receptor activator of nuclear factor-kappa-B (RANK-L). Because neutrophils play a crucial role in chronic inflammation, the goal of this study was to determine whether proteins of the RANK/RANK-L pathway are expressed by synovial fluid (SF) neutrophils from pa...