Crossminton is a sport that combines elements of squash, badminton and tennis, creating new sport, which currently being played all over the world. The aim our study was to identify compare bilateral differences in internal external rotation glenohumeral joint crossminton players. subject were 13 players from Slovak Republic (25.1±9.3 years; 172.8±9.1 cm; 71.8±16.1 kg). range motion (IR-ROM) (E...

Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra numerical range V...

The numerical range W (A) of an n×n matrix A is the collection of complex numbers of the form x∗Ax, where x ∈ C is a unit vector. It can be viewed as a “picture” of A containing useful information of A. Even if the matrix A is not known explicitly, the “picture” W (A) would allow one to “see” many properties of the matrix. For example, the numerical range can be used to locate eigenvalues, dedu...

The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine section of the semidefinite cone, is always dual to the numerical range of a matrix, which is therefore an affine projection of the semidefinite con...