A difficult problem for me. let ( ) = A so that and . Prove that det A > 0
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Originally Posted by kezman A difficult problem for me. let ( ) = A so that and . Prove that det A > 0 How can these and both true simultaneously?
Sorry I forgot: the first condition is for the second condition is for all
Originally Posted by kezman Sorry I forgot: the first condition is for the second condition is for all So did you mean if and ? But this can't be true, a counterexample, where the sum of all entries is 1>0 and . Please double check again
Originally Posted by kezman A difficult problem for me. let ( ) = A so that for and for 1≤i≤n. Prove that det A > 0 Such a matrix is called diagonally dominant. The result that you want follows from the Gershgorin circle theorem.
Last edited by Opalg; May 19th 2008 at 03:19 AM.
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