AN INVERSE PROBLEM FOR THE k-RANK NUMERICAL RANGE

作者：Katsouleas Georgios^*; Maroulas John

来源：SIAM Journal on Matrix Analysis and Applications, 2016, 37(3): 1022-1037.

DOI：10.1137/15M1009342

• higher rank numerical range
• compressions
• inverse problem

For an n x n matrix A and an integer k is an element of [1, n], the concept of the higher rank numerical range Lambda(k)(A) = {z is an element of C : V*AV = zI(k), V is an element of C-nxk, V*V = I-k} has been introduced in relation to the study of error correcting codes and has been extensively studied. In this paper, an inverse problem for Lambda(k)(A) is considered, where, for a given point z is an element of Lambda(k)(A), we investigate the construction of a generating isometry V is an element of C-nxk for z, i.e., such that V*AV = zI(k). Under this scope, the notion of a covering number for higher rank numerical range points is introduced, generalizing a corresponding definition for k = 1.

• 出版日期2016