Cholesky Decomposition (How to equate matrix element by element)

Referring to the Cholesky Method.

Let A be the input symmetric matrix Let X be the product of lower triangular matrix and its transpose. Suppose A is a 3x3 symmetric matrix : [1,2,3;2,5,6;3,6,1] Then X is [a^2 ,ab,ac ; ab,b^2 + d^2,bc+de ;ac, bc+de ,c^2 +e^2 +f^2] How can I compare A and X, element by element so that i will find the values of a,b,c,d,e,f I just cant type A=X it says error and it doesnt compute the values, i need to find the values of the said variables so that the output will show two matrices one is the lower triangular matrix with the values of a,b,c,d,e,f and the other one is its transpose *we are not allowed to use chol function or built-in functions Thank you very much.

[Torsten]

How do you want to generalize your concept for an (nxn)-matrix A for large n ? Do you really want to solve a nonlinear system of equations of size (n^2-n)/2+n = n*(n+1)/2 to make a Cholesky decomposition ? That's overkill.

Best wishes

Torsten.