Narrower eigenbounds for Hadamard products (Q1369321)

The author considers the Hadamard product of two positive semidefinite matrices of order \(n\). An ``augmented'' Schur theorem is proved which yields a specific bound for each eigenvalue of the Hadamard product. The result improves the classical global bounds by \textit{I. Schur} in ``Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen, J. Reine und Angewandte Math. 140, 1-28 (1911). The results should be interesting for specific considerations in statistics.