What does the error “arguments imply differing number of rows: x, y” mean?

Your data.frame mat is rectangular (n_rows!= n_cols).

Therefore, you cannot make a data.frame out of the column- and rownames, because each column in a data.frame must be the same length.

Maybe this suffices your needs:

require(reshape2)
mat$id <- rownames(mat) 
melt(mat)

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