Let P, Q ∈ C be two normal {k+1}-potent matrices, i.e., PP ∗ = P P, P k+1 = P , QQ = QQ, Q = Q, k ∈ N. A matrix A ∈ C is referred to as generalized reflexive with two normal {k + 1}-potent matrices P and Q if and only if A = PAQ. The set of all n × n generalized reflexive matrices which rely on the matrices P and Q is denoted by GR(P,Q). The left and right inverse eigenproblem of such matrices ...

In this paper we continue our investigations. begun in the previous paper, of describing the solution sets of constrained extremum problems inf Au). l&l-‘(p) (*) where fand f are twice continuously differentiable functionals on a reflexive Banach space V, and r-‘(p) denotes the level set of the functional f with value p E R. Considering p as a parameter in (*) we obtain results concerning the c...

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 discuss an operator equation Kf = g where X, Y are reflexive Banach spaces of functions in bounded domains Ω ⊂ RN and Ω0, and K : X −→ Y has no continuous inverse. Let V and V1 be another reflexive Banach spaces of functions in Ω and D ⊂ Ω respectively such that the embedding V ⊂ X is continuous. In order to stably reconstruct g by noise data gδ with ‖g − gδ‖Y ≤ δ: noise level, we consider t...