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).