The following hack might help:
x <- as.matrix(read.table(textConnection("X1053_at X117_at X121_at X1255_g_at X1294_at X1316_at X1320_at
X1053_at 0 0.00040833 0.052000448 0.101470422 0.00040833 0.223143551
X117_at 0.00040833 0 0.00040833 0.174561677 0.174561677 0.034204976
X121_at 0.052000448 0.00040833 0 0.020410997 0.010309644 0.034204976
X1255_g_at 0.101470422 0.174561677 0.020410997 0 0.020410997 0.174561677
X1294_at 0.00040833 0.174561677 0.010309644 0.020410997 0 0.101470422
X1316_at 0.223143551 0.034204976 0.034204976 0.174561677 0.101470422 0
X1320_at 0.074226329 0.134540323 0.052000448 0.00368703 0.020410997 0.101470422"), header=TRUE, row.names=1))
# not sure if this is correctly aligned as you have 7 column names for 6 columns
as.data.frame(as.table(x))
Result:
Var1 Var2 Freq
1 X1053_at X117_at 0.00000000
2 X117_at X117_at 0.00040833
3 X121_at X117_at 0.05200045
4 X1255_g_at X117_at 0.10147042
5 X1294_at X117_at 0.00040833