results the results of this study showed high reliability and validity of smartphone in regarding ug with icc > 0.95. the highest reliability for both methods was in elbow supination and the lowest was in the elbow flexion (0.84). objectives the study was designed to compare the smartphone inclinometer-based app and ug in evaluation of rom of elbow. materials and methods the maximum rom of elbo...

Let A be an n× n normal matrix, whose numerical range NR[A] is a k -polygon. If a unit vector v ∈ W ⊆ Cn, with dimW = k and the point v∗Av ∈ IntNR[A], then NR[A] is circumscribed to NR[P∗AP], where P is an n× (k− 1) isometry of {span{v}}⊥ W → Cn, [1]. In this paper, we investigate an internal approximation of NR[A] by an increasing sequence of NR[Cs] of compressed matrices Cs = R∗s ARs, with R∗...

Some algebraic properties of the sharp points of the numerical range of matrix polynomials are the main subject of this paper. We also consider isolated points of the numerical range and the location of the numerical range in a circular annulus.

The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces trM M and trM M are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5 5 nilpotent matrix has circular numerical ran...

Some fundamental examples are provided, which are useful to study the topological properties of the numerical range of matrix polynomials. Mathematics Subject Classification: 47A12, 47A56