A new lower bound on the eigenvalues of a Hadamard product is given in terms of the rank, effective condition number, diagonal entries, and principal submatrix eigenvalues of the two factors.
Schur, Bemerkungen zur Theorie der beschr¨ ankten Bilinearformen mit unendlich vielen Ver¨ anderlichen, Journal f¨ ur die reine und angewandte Mathematik 140 (1911) 1–28
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Positivity of a Hadamard Product
A new lower bound on the eigenvalues of a Hadamard product is given in terms of the rank, effective condition number, diagonal entries, and principal submatrix eigenvalues of the two factors.