Going back from a correlation matrix to the original matrix I have N sensors which are been sampled M times, so I have an N by M readout matrix. If I want to know the relation and dependencies of these sensors simplest thing is to do a Pearson's correlation which gives me an N by N correlation matrix. 
Now let's say if I have the correlation matrix but I want to explore tho possible readout space that can lead to such correlation matrix what can I do? 
So the question is: given an N by N correlation matrix how you can get to a matrix that would have such correlation matrix?
Any comment is appreciated. 

May I tell you guys my silly solution to this problem? Only if you won't laugh at me! I thought I need to explore this space so I want to randomly sample it (the space of sensor readings). I know what the correlation matrix should look like and I know that the sensor readings are coming from a Gaussian distribution. So I generated a random N by M matrix and started tweaking the values in small steps. and check if each change moves the matriv toward the target or away and kept the changes toward the target. So I choose a random cell in this matrix and increase it by 10% and calculate the correlation matrix and compare it to the target correlation matrix the difference is smaller than what it was before the 10% increase I keep the change and move to next randomly selected cell and continue until I get close enough to the target correlation matrix.  This method, although it is silly, works well and I can get different samples of the sensor reading space.  What you guys think?! In practice I am working on rather large matrices like N = 8000, M = 1000  
