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...

In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.–D. Choi et al., Rep. Math. Phys. 58, 77 (2006); Lin. Alg. Appl. 418, 828 (2006)], is a natural tool for studying a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to o...

This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In this paper it is shown that stronger results can be obtained for the complex Hermitian case. In part...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulted nuclear norm and `1 norm related minimization problem can also be efficiently solved by many recently developed...