Constructing Matrix with Normal Distribution

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I have a vector given whereby each element of the vector is assumed to be the average of one of a matrix' rows. Now I want to construct the matrix belonging to this vector, whereby the elements of the matrix should be normally distributed. Furthermore, the matrix is the result of a Fisher z-transformation on a correlation matrix, so these constraints can be used too. How could I progress? My first idea was to use some optimization, but possibly there is a more theoterical/analytic approach to that?