Comparing a matrix to its off-diagonal part

Bhatia, Rajendra ; Davis, Chandler ; Choi, Man-Duen (1989) Comparing a matrix to its off-diagonal part Operator Theory: Advances and Applications, 40-41 . pp. 151-164. ISSN 0255-0156

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Let O be the operation which for any n × n complex matrix replaces all its diagonal entries by zeroes. For various matrix norms, we study max A |||OA|||/|||A|||. Upper and lower bounds are obtained, but they agree only for the c p norms with p = 1, 2, ∞. For these latter norms, the value of the maximum is also obtained with A restricted to the subset A ≥ 0.

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