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.
Bounds on inverse elements of Hermitian matrices
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linear-algebra
matrices
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1if you are more specific, you can (possibly) get more help... – 2011-03-29
1 Answers
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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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0Thanks for your answer. I didn't expect such a succinct proof sketch. – 2011-03-30