Create dataframe from a matrix

You can use stack from the base package. But, you need first to coerce your matrix to a data.frame and to reorder the columns once the data is stacked.

mat <- as.data.frame(mat)
res <- data.frame(time= mat$time,stack(mat,select=-time))
res[,c(3,1,2)]

  ind time values
1 C_0  0.0    0.1
2 C_0  0.5    0.2
3 C_0  1.0    0.3
4 C_1  0.0    0.3
5 C_1  0.5    0.4
6 C_1  1.0    0.5

Note that stack is generally more efficient than the reshape2 package.

If you change your time column into row names, then you can use as.data.frame(as.table(mat)) for simple cases like this.

Example:

data <- c(0.1, 0.2, 0.3, 0.3, 0.4, 0.5)
dimnames <- list(time=c(0, 0.5, 1), name=c("C_0", "C_1"))
mat <- matrix(data, ncol=2, nrow=3, dimnames=dimnames)
as.data.frame(as.table(mat))
  time name Freq
1    0  C_0  0.1
2  0.5  C_0  0.2
3    1  C_0  0.3
4    0  C_1  0.3
5  0.5  C_1  0.4
6    1  C_1  0.5

In this case time and name are both factors. You may want to convert time back to numeric, or it may not matter.