Does there exist $x$ such that $\|Ax\|=\|A\|$, where $$\|A\|=\sup\{|d|:d\text{ is eigenvalue of of the symmetric matrix $A$}\}$$ Why does it suffice to find an eigenvector of the eigenvalue I found, or does it not?
2026-04-17 08:20:46.1776414046
Eigenvectors when the eigenvalue if the norm of the matrix.
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I believe you want to know if there exists $x$ with $\|x\|=1$ and $\|A(x)\|=\|A\|$. A symmetric matrix is diagonalizable, so if $d$ is the bigger value, there exists $x$ such that $A(x)=dx$. You can take $x$ such that $\|x\|=1$.