--- John Randall <[EMAIL PROTECTED]> wrote: > Thanks to Henry and Raul for their solutions. I am still slightly > hazy as to why one can get away with &. rather than &.: .
Why &.: not &. was needed? Because its right verb ^ is atomic, so +/ only "sees" atomic results of ^ . Now @:| in +/@:|&. makes rank _ thus 2 (^&)(+/@:|&.) 2 3 4 5.38516 Same can be done with hook (^~|) as in non-conjunctional norm: 2 ([ %: +/@(^~ |)) 2 3 4 5.38516 Cf 2 (([ %: +/@:^~) |) 2 3 4 5.38516 > Henry Rich wrote: > > I don't know the exact definition of n-norm > > I should have explained. > > The Lp norm of a vector v is p%:(| v)^p, an obvious case for some form or rather p%:+/(| v)^p ? > of under. The L2 norm just measures the Euclidean distance of a point > from the origin. You can also define the Linfinity norm of v to be > the limit as p goes to infinity of Lp(v), and this has the simple form > >./ | v . All of these norms are equivalent. > > The Linfinity is used a lot in linear algebra, since you also want > matrix norms. If n is a vector norm and A is a matrix, then you can > get a matrix norm by defining n(A) to be the maximum of n(Av), where > n(v)=1. For the infinity norm, this is just >./ +/"1 A. The > corresponding L2 norm is much more difficult to calculate. > > Best wishes, > > John > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ____________________________________________________________________________________ Yahoo! oneSearch: Finally, mobile search that gives answers, not web links. http://mobile.yahoo.com/mobileweb/onesearch?refer=1ONXIC ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
