Moment of a subspace and joint numerical range

KLOBOUK, ABEL H.; VARELA, ALEJANDRO

LINEAR AND MULTILINEAR ALGEBRA

TAYLOR & FRANCIS LTD

Año: 2022 p. 1 - 34

0308-1087

For a subspace S of Cn and a fixed basis, we study a compact and convex set that we call the moment of S. This set is relevant in the determination of minimal hermitian matrices (those that have minumum spectral norm  under perturbations of diagonal real matrices. We describe extremal points and certain curves of the moment of S in terms of principal vectors that minimize the angle between S and the coordinate axes of the fixed basis. We also relate this set to the joint numerical range W of n rank one hermitian matrices constructed certain orthogonal projections and the fixed basis used. This connection provides a new approach to the description of the moment set and to minimal matrices. As a consequence, the intersection of two of these joint numerical ranges corresponding to orthogonal subspaces allows the construction or detection of a minimal matrix.