Find minimal a for PSD of 3x3 matrix
Capital OneData Scientist · Technical Screen
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This question evaluates understanding of linear algebra concepts such as eigenvalues, matrix definiteness, and spectral properties by asking for the minimal real parameter a that makes a symmetric 3×3 matrix with ones on the diagonal and constant off-diagonal entries positive semidefinite.
Find the smallest real a such that the symmetric matrix with ones on the diagonal and a on all off-diagonal entries, A = [[1, a, a], [a, 1, a], [a, a, 1]], is positive semidefinite. Justify using eigenvalues (or Sylvester’s criterion), showing all steps.
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