It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

We consider here passive mechanical wrists, capable of imparting a desired dumping matrix to a grasped workpiece. Previous work 112. 131 has shown how to select a dumping matrix such that an assembly operatwn can be modc force-guided Thc passive mechanical wrist is to be progmnvnable it can adopt a widc range of damping matrices by virtue of a number of t u d e dampers which inrcrconneet the jo...

The higher rank numerical range is useful for constructing 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 rank-k 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 the higher rank numeri...

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 ...

in this paper we study the impact of minkowski metric matrix on a projection in theminkowski space m along with their basic algebraic and geometric properties.the relationbetween the m-projections and the minkowski inverse of a matrix a in the minkowski spacemis derived. in the remaining portion commutativity of minkowski inverse in minkowski spacem is analyzed in terms of m-projections as an a...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invar...

The stability radius of a matrix polynomial P (λ) relative to an open region Ω of the complex plane and its relation to the numerical range of P (λ) are investigated. Using an expression of the stability radius in terms of λ on the boundary of Ω and ‖P (λ)−1‖2, a lower bound is obtained. This bound for the stability radius involves the distances of Ω to the connected components of the numerical...