Comparing a Matrix to its Off-Diagonal Part
Rajendra Bhatia, Man-Duen Choi, Chandler Davis · Birkhäuser Basel eBooks · 1989
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.