Question

Estimate the eigen values of the matrix:

 

equation

 

using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.

12 Sep 2025
Answer :
Word Count : 221
For estimating the eigenvalues of a matrix using Gerschgorin bounds, each eigenvalue lies within at least one of the Gerschgorin discs. Consider a square matrix $A = [a_{ij}]$ of order $n$. The Gerschgorin discs are defined for each row as $D_i = \{z \in _______ ________ _______ _____ _____ ___ _________ ___ _____ ________ _____.
______ ____ ____ ____ _________ ___ ______.
__________ ____ ______ ____ _____ _________ _________.
_______ ___ _______ __________ _____ _____ ___ ___.
_____ ________ ________ ____ _____.
______ ________ ________ ________ __________ _______ _____ ______.
______ __________ _____ ___ ___ _____ ____ ________ ______.
_________ _______ ___ _______ ________ ________ ______ _________.
_____ ________ _____ _______ ________ ________ _________ ________.
_________ __________ ___ ___ _____ ____.
_______ _________ ____ ______ _____ _______ ________ ________ ___.
_______ ________ ______ ____ _______ ______.
_________ _____ _______ _________ _____ _______ _________.
_____ ______ ____ ______ _____ ____ ___ ___ _________ ___.
____ __________ _____ _____ _______ ________ __________ _________ _______ ______ ________ ___.
____ ______ ______ _____ _____ ______ ___.
_____ _____ _____ _________ __________ ________ ___ _________ _____ _______.
______ _____ __________ _____ __________ _______ _________ ______ _____ _____ _______.
________ ___ ______ _______ ________ ________.
__________ ____ _________ ___ __________ ___ __________ __________ _________ ____.
______ ______ ______ ________ ___ ___ _________ _______ ____ __________.
_________ ____.
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