I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., `SS = A`) I'm trying :
 
 
 Ftemp = {{F11, F12, F13, 0, 0}, 
 {F12, F22, 0, 0, 0}, 
 {F13, 0, F33, 0,F35}, 
 {0, 0, 0, F44, F45}, 
 {0, 0, F35, F45, F55}}

All the elements in the matrix real. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is which entries in the resulting solution will be different from zero (and thus which entries will be zero).