Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., R = R = R−1 = ±Im and S = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize ‖AX−Z‖2+‖Y HA−WH‖2, a...

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another ...

Editorial Summary In her contribution »Reflexive, Reflexivity, and the Concept of Reflexive Design« Margitta Buchert frames notion reflexive design research, pitting various underlying concepts against one another forming framework for research. As such, she emphasizes punctuated distinction reflection as an integrated component research reflexion alignment attitude. this sense highlights recip...

Reflexive saccades (fast eye movements) and voluntary saccades activate overlapping parts of the oculomotor system. It is assumed that striatal dopamine depletion in Parkinson's disease (PD) only affects the voluntary saccadic system and that the often-reported facilitation of the reflexive saccadic system in PD is secondary to impairment of the voluntary saccadic system. If this assumption is ...

We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Zn(L1(G),X), the space of bounded ncocycles from L1(G)(n) into X, where L1(G) is the group algebra of a locally compact group G and X is a Banach L1(G)-bimodule. We show that Zn(L1(G), X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almos...

An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...