GATE EE 2016 Set 1 — Question 12
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
Consider a matrix with every element being equal to 1. Its only non-zero eigenvalue is ____.
Correct answer
3 to 3
Solution
For an matrix where every element is 1, the rank of the matrix is 1. This implies that there is only one non-zero eigenvalue. The sum of the eigenvalues of a matrix is equal to its trace (the sum of the diagonal elements). For a matrix of all 1s, the trace is . Since all other eigenvalues are zero, the only non-zero eigenvalue must be 3.
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