Question on matrix calculation

Hello again,

Ley say I have 1 matrix and 1 data frame:

mat <- matrix(1:15, 5)
match_df <- data.frame(Seq = 1:5, criteria = sample(letters[1:5], 5, replace = T))
mat

[,1] [,2] [,3]
[1,]    1    6   11
[2,]    2    7   12
[3,]    3    8   13
[4,]    4    9   14
[5,]    5   10   15

match_df

Seq criteria
1   1        c
2   2        e
3   3        c
4   4        c
5   5        d

Now I want to get the column-sums of 'mat' based on the unique
elements of match_df[,'criteria']

Therefore based on the 'match_df', my resulting matrix will have 3
rows (because the unique elements here are 'c, e, & d'). And.........

1st row will be column sums for mat[c(1,3,4), ]
2nd row will be column sums for mat[c(2), ]
3rd row will be column sums for mat[c(5), ]

I want to get a general framework, so that I can implement that in
some big arbitrary matrix.

Can somebody give me some pointer?

Thanks and regards,