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 solution using bgoldst's definition of df1 and df2

sapply(unique(c(as.matrix(df2))),function(x) sum(df1[df2==x]))

Gives

#A  B  C  D  E  F  G 
#8 13 13 28 10 18  2 

(Not quite the format that you wanted, but maybe it's ok...)