Distance from projections To nilpotents
|Title||Distance from projections To nilpotents|
|Author(s)||Gordon W. MacDonald|
|Journal||Canadian Journal of Mathematics - Journal Canadien de Mathematiques|
|Abstract||The distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k x k matrices with the usual operator norm, is shown to be sec(pi/(k+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k x k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of 3 x 3 matrices is root(3-root 5)/2.|
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