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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).
Transcribed Image Text: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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