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...Unsolved matrix problems xingzhi zhan math ecnu edu cn department of mathematics east china normal university let denote the spectral radius i e maximum modulus eigenvalues a hadamard product entry wise matrices conjecture if b are nonnegative same order then ab remark sept has been proved by k m r audenaert versus conventional for non negative linear algebra appl and horn f zhang bounds on or positive semidenite electron j respectively z huang extended this inequality to case more in his paper norm products appear laa n set number s integers max ak posed following two at seminar problem determine that attain is solved wu digraph with ij vertices which an arc only gives bijection between digraphs graph theoretic interpretation d be each pair dthere most one walk length from what arcs we may also consider analogous symmetric pairs there exactly...