Linear n-widths of diagonal matrices in the average and probabilistic settings ✩

Exact values of the average linear n-widths with respect to the standard Gaussian measure on Rm are determined for diagonal matrices, and are applied to deduce several new results on linear n-widths in the average and probabilistic settings, including the sharp upper and lower estimates of the linear (n, δ)-widths of diagonal matrices. © 2012 Elsevier Inc. All rights reserved.