Write the formula for the condition number of A, ||A|A¹||, in terms of the eigenvalues of A when A is s.p.d. Given a small (2 x 2) matrix A = its eigenvalues and its inverse, compute its condition number using one of the norms. and investigate what happens with the condition number when € → 0. 1 [date]
Write the formula for the condition number of A, ||A|A¹||, in terms of the eigenvalues of A when A is s.p.d. Given a small (2 x 2) matrix A = its eigenvalues and its inverse, compute its condition number using one of the norms. and investigate what happens with the condition number when € → 0. 1 [date]
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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![(6) Write the formula for the condition number of \( A \), \( \|A\|\|A^{-1}\| \), in terms of the eigenvalues of \( A \) when \( A \) is s.p.d. Given a small (2 x 2) matrix
\[
A = \begin{bmatrix} 1 & 1 \\ 1 & 1+\epsilon \end{bmatrix},
\]
its eigenvalues and its inverse, compute its condition number using one of the norms, and investigate what happens with the condition number when \( \epsilon \rightarrow 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe080acd7-15b7-4773-a575-c0d96605e182%2F2dfaac0b-e91e-4905-8a6c-38ec9e41ca0f%2Fwrrfji7_processed.png&w=3840&q=75)
Transcribed Image Text:(6) Write the formula for the condition number of \( A \), \( \|A\|\|A^{-1}\| \), in terms of the eigenvalues of \( A \) when \( A \) is s.p.d. Given a small (2 x 2) matrix
\[
A = \begin{bmatrix} 1 & 1 \\ 1 & 1+\epsilon \end{bmatrix},
\]
its eigenvalues and its inverse, compute its condition number using one of the norms, and investigate what happens with the condition number when \( \epsilon \rightarrow 0 \).
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