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Let $A$ be an $N$ by $N$ Hermitian matrix with elements $a_{ij}$. What will be the bound on the elements $b_{ij}$ where $B=A^{-1}$? If $A$ is a diagonal matrix, solution is trivial. Also for tri-diagonal matrix, bounds exists.

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    if you are more specific, you can (possibly) get more help...2011-03-29

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If H is a Hermitian matrix whose eigenvalues all have absolute value $\ge r$, then the matrix elements of $H^{-1}$ are bounded by $1/r$.

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    Thanks for your answer. I didn't expect such a succinct proof sketch.2011-03-30