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Apr
11
comment Lower bound for divergence of matrix spectrum
Now it is better (however, you should replace $i + 1$ by $j$). But I don't know ways to estimate $\min_{i \ne j} |\lambda_i - \lambda_j|$ for a matrix in rather general form.
Apr
11
suggested suggested edit on Lower bound for divergence of matrix spectrum
Apr
11
revised Lower bound for divergence of matrix spectrum
added 4 characters in body
Apr
11
comment Lower bound for divergence of matrix spectrum
Thanks for suggestion. I will edit my question to make clear I want some $c > 0$.
Apr
11
comment Lower bound for divergence of matrix spectrum
Really, isn't helpful. It is a bound of the form $N c$.
Apr
11
revised Lower bound for divergence of matrix spectrum
Make notation clear
Apr
11
suggested suggested edit on Lower bound for divergence of matrix spectrum
Apr
11
comment Finding expected value of variance estimator (sum expansion problem)
At the right hand side we expand mean at the left hand side. We have $n$ quadratic first, they are collected in the first sum. Cross-terms $\sum_{i \ne j} (X_i - \mu) (X_j - \mu) = 2 \sum_{i = 1}^{n - 1} \sum_{j > i} (X_i - \mu) (X_j - \mu)$ are collected in the second sum at the right hand side.
Apr
11
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