Examnple: Determine the Gersgorin disks for the matrix 4 1 A = 2 2 -2 0 10

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 1CEXP
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Examnple: Determine the Gersgorin disks for the matrix
4 1 2
A
2 2
=
-2 0 10
The Gersgorin disks are
R = {z € C : |2 – 4| < 3} , R, = {z E C : |2 – 2| < 2} , R3 = {z € C : |2 –
4|< 3}, R2 = {2 E C : 2
2| < 2}, R3 = {: E C: 2
Since RUR2 and R3 are disjoint, there are two eigenvalues in R1U R2 and or
RI
One eigenva
Transcribed Image Text:Examnple: Determine the Gersgorin disks for the matrix 4 1 2 A 2 2 = -2 0 10 The Gersgorin disks are R = {z € C : |2 – 4| < 3} , R, = {z E C : |2 – 2| < 2} , R3 = {z € C : |2 – 4|< 3}, R2 = {2 E C : 2 2| < 2}, R3 = {: E C: 2 Since RUR2 and R3 are disjoint, there are two eigenvalues in R1U R2 and or RI One eigenva
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