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  "path": "/abs/2605.03772v1",
  "publishedAt": "2026-05-06T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Lan V. Truong",
    "M. H. Duong"
  ],
  "textContent": "**Authors:** Lan V. Truong, M. H. Duong\n\nWe 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.",
  "title": "On the Induced Norms of Matrices and Grothendieck problems"
}