How to sum over diagonals of data frame

Question

Say that I have this data frame:

     1   2   3   4      
100  8   12  5   14 
99   1   6   4   3   
98   2   5   4   11  
97   5   3   7   2   

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Answer 1

Another aggregate variation, avoiding the formula interface, which actually complicates matters in this instance:

aggregate(list(Sum=unlist(dat)), list(Group=LETTERS[c(row(dat) + col(dat))-1]), FUN=sum)

#  Group Sum
#1     A   8
#2     B  13
#3     C  13
#4     D  28
#5     E  10
#6     F  18
#7     G   2