GATE 2014 CS (CS1) – Question 15
Find the dot product of eigenvectors corresponding to any pair of different eigenvalues of a 4 × 4 symmetric positive-definite matrix.
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Correct answer: 0 to 0
Explanation
For symmetric A, vᵀAw=(Av)ᵀw. If Av=λv and Aw=μw, this implies(μ−λ)vᵀw=0. Distinct eigenvalues therefore force **vᵀw=0**. Positive definiteness is stronger than needed for this orthogonality result.