Question: Cholesky Decomposition for a symbolic matrix

January 30 2013 manueleleonelli 10
Maple

1

I wrote down a covariance matrix through the following command:

 A := Matrix([[a, b], [b, c]], shape = symmetric, attributes = [positive_definite]);

and then I computed the Cholesky decomposition of this matrix using afterwards the command simplify as well
B := LUDecomposition(A, method = Cholesky)
C:=simplify(%)
What I obtained is this matrix
Matrix(2, 2, {(1, 1) = sqrt(a), (1, 2) = 0, (2, 1) = conjugate(b)/sqrt(a), (2, 2) = sqrt(c-abs(b^2/a))})
Is there any way in which I can tell the software that some of the entries are positive and real, so that I don't obtain any absolute value or conjugate??
 
The problem is that when I then multiply C with its transpose I don't exactly obtain the matrix A, as it should be.. It is the same but it is written in terms of conjugates and absolute values.

Can you help me?
Manuele 
Please Wait...