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$\begingroup$ typos? 2nd line of definition "i=1≤i≤n", and next line should be $x_i^{j-\color{red}i}$? It would also be helpful to include M explicitly for n=3, that is easier to see than reading a formula with cases! $\endgroup$Wolfgang– Wolfgang2019-01-25 11:39:20 +00:00Commented Jan 25, 2019 at 11:39
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$\begingroup$ Thank you for the suggestion, I fixed the typos and put the example $\endgroup$F.Battistoni– F.Battistoni2019-01-25 12:47:39 +00:00Commented Jan 25, 2019 at 12:47
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$\begingroup$ For the given matrix M, I share your skepticism, as f evaluates to 0 at the extreme points. Can you say anything about the matrices similar to M? It is possible that locally the similar matrices might do the job. Gerhard "Monomials Can Seem Very Independent" Paseman, 2019.01.25. $\endgroup$Gerhard Paseman– Gerhard Paseman2019-01-25 17:31:33 +00:00Commented Jan 25, 2019 at 17:31
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