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Matriceshard
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For a 3×33 \times 33×3 matrix AAA with eigenvalues λ1,λ2,λ3\lambda_1, \lambda_2, \lambda_3λ1​,λ2​,λ3​, suppose tr(A)=λ1+λ2+λ3=12\text{tr}(A) = \lambda_1 + \lambda_2 + \lambda_3 = 12tr(A)=λ1​+λ2​+λ3​=12 and tr(A2)=λ12+λ22+λ32=50\text{tr}(A^2) = \lambda_1^2 + \lambda_2^2 + \lambda_3^2 = 50tr(A2)=λ12​+λ22​+λ32​=50. What is the value of 2∑i<jλiλj2\sum_{i < j} \lambda_i \lambda_j2∑i<j​λi​λj​?