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Results tagged with eigenvalues
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user 475215
eigenvalues of matrices or operators
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Prove that sum of eigenvalues of the inverse of an nxn correlation matrix A is greater than ...
I stuck on this question and here is my thoughts:
So we have a nxn correlation matrix A with eigenvalues: λ_1,λ_2,...,λ_n
1.According to the property of correlation matrix, (λ_1)+(λ_2) + ... + (λ_n) = … n
2.According to the property of inverse matrix, Let B = $A^{-1}$, then B has eigenvalues: 1/λ_1,1/λ_2,...,1/λ_n
3.Now the question has been transformed into: Prove that 1/λ_1+1/λ_2+...+1/λ_n $\geq$ λ …
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