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Bibliographic Details
Main Authors: Truong, Lan V., Duong, M. H.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.03772
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Table of Contents:
  • We study the induced matrix norm $\|\bA\|_{q \to r}$, whose exact value has been known only in a few classical cases. Determining this norm has long been regarded as difficult due to the highly non-convex nature of its variational definition. Existing works offer numerical estimates or analytic bounds but no exact formula. In this paper we present a purely analytic framework that determines $\|\bA\|_{q \to r}$ exactly for all $q, r \ge 1$ for several classes of important matrices. For these matrices, using a direct connection between the induced norms and Grothendieck problems, our results also simultaneously provide exact values for the later.