Summarizing multiple columns with data.table

You can use a simple lapply statement with .SD

dt[, lapply(.SD, sum, na.rm=TRUE), by=category ]

   category index        a        b        z         c        d
1:        c    19 51.13289 48.49994 42.50884  9.535588 11.53253
2:        b     9 17.34860 20.35022 10.32514 11.764105 10.53127
3:        a    27 25.91616 31.12624  0.00000 29.197343 31.71285

If you only want to summarize over certain columns, you can add the .SDcols argument

#  note that .SDcols also allows reordering of the columns
dt[, lapply(.SD, sum, na.rm=TRUE), by=category, .SDcols=c("a", "c", "z") ] 

   category        a         c        z
1:        c 51.13289  9.535588 42.50884
2:        b 17.34860 11.764105 10.32514
3:        a 25.91616 29.197343  0.00000

This of course, is not limited to sum and you can use any function with lapply, including anonymous functions. (ie, it's a regular lapply statement).

Lastly, there is no need to use i=T and j= <..>. Personally, I think that makes the code less readable, but it is just a style preference.

Documentation

See ?.SD, ?data.table and its .SDcols argument, and the vignette Using .SD for Data Analysis.

Also have a look at data.table FAQ 2.1.