and D be a diagonal matrix D = diag(A₁,..., An) such that
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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Question
M6
Transcribed Image Text:Let A € M₂ (C) be a diagonalizable matrix, P be an invertible matrix,
and D be a diagonal matrix D = diag(A₁,..., An) such that
A = PDP-¹,
and let || || be a matrix norm such that
||diag(a₁,..., an) || = = max |ai|,
1≤i≤n
for every diagonal matrix. Then for every perturbation matrix AA, if we write
B₁ = {z € C | |z − λi| ≤ cond(P) ||AA||},
for every eigenvalue λ of A+ AA, we have
n
XE Ů BK
k=1
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