For any real vector , let denote the components of in non-increasing order.
For , we say that is majorized by , or majorizes , if
A common notation for “ is majorized by ” is .
A canonical example is that, if , are non-negative real numbers such that their sum is equal to 1, then
In general, vaguely means that the components of is less spread out than are the components of .
G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd edition, 1952, Cambridge University Press, London.
A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, 1979, Acadamic Press, New York.
|Date of creation||2013-03-22 14:30:22|
|Last modified on||2013-03-22 14:30:22|
|Last modified by||rspuzio (6075)|