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I have the following equation:

[tex]\gamma=\frac{1}{\frac{1}{N}\sum_{n=1}^N|\lambda_n|^{-2}}[/tex]

where lambdas are the eigenvalues of an N-by-N circulant matrix A.

I used two properties to bound the above equation:

[tex]\frac{1}{N}\sum_{n=1}^N|\lambda_n|^{-2}\geq\left(\prod_{n=1}^N|\lambda_n|^{-2}\right)^{1/N}[/tex]

[tex]\sum_{n=1}^N|\lambda_n|^{-2}\leq\left(\sum_{n=1}^N|\lambda_n|^{2}\right)^{-1}[/tex]

Are these two bounds correct?

Thanks

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# Arithmetic and Geometric Mean

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