Theorem 9.7.5. [Weyl Interlacing Theorem] Let A, B = Mn (C) be Hermitian matrices. Then,Ak (A) + A₁(B) ≤ λk (A + B) ≤ λk (A) + λn (B). In particular, if B = P*P, for some matrix P,then X (A + B) ≥ Ak(A). In particular, for z E C", λk (A+zz*) ≤ λk+1(A).

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Let A, B & Mn (C) be Hermitian matrices. Then

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 18E: Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix...

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Question

Theorem 9.7.5. [Weyl Interlacing Theorem] Let A, B = Mn (C) be Hermitian matrices. Then,
Ak (A) + A₁(B) ≤ λk (A + B) ≤ λk (A) + λn (B). In particular, if B = P*P, for some matrix P,
then X (A + B) ≥ Ak(A). In particular, for z E C", λk (A+zz*) ≤ λk+1(A).

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