Let Tmn be a BTTB matrix with a generating function f(x, y) ∈ C2π×2π. Let λmin(Tmn) and λmax(Tmn) denote the smallest and largest eigenvalues of Tmn, respectively. Then we have fmin ≤ λmin(Tmn) ≤ λmax(Tmn) ≤ fmax, where fmin and fmax denote the minimum and maximum values of f(x, y), respectively. In particular, if fmin > 0, then Tmn is positive definite

Let Tmn be a BTTB matrix with a generating function f(x, y) ∈ C2π×2π. Let λmin(Tmn) and λmax(Tmn) denote the smallest and largest eigenvalues of Tmn, respectively. Then we have fmin ≤ λmin(Tmn) ≤ λmax(Tmn) ≤ fmax, where fmin and fmax denote the minimum and maximum values of f(x, y), respectively. In particular, if fmin > 0, then Tmn is positive definite

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.1: Matrices And Vectors

Problem 5P

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