GATE 2018 CS – Question 27
Consider a matrix $A=uv^T$ where $u=\begin{pmatrix}1\\2\end{pmatrix}$, $v=\begin{pmatrix}1\\1\end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ________.
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Correct answer: 3
Explanation
$A$ has rank 1, so its only non-zero eigenvalue is its trace, $v^Tu=1+2=3$.