GATE 2021 CS – Question 62
Consider the following matrix.
$\begin{pmatrix} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{pmatrix}$
The largest eigenvalue of the above matrix is ______.
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Correct answer: 3
Explanation
The matrix is J - I with J the all-ones matrix. J has eigenvalues 4, 0, 0, 0, so J - I has eigenvalues 3, -1, -1, -1. The largest is 3.