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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...

Ok If R is the Cholesky decomposition of the Covariance matrix then I need:

i) Cov=R*R'
ii) R'=R

I can show that i) indeed holds but ii) does not seem to work. Why?

restart:
with(LinearAlgebra):
Cov := Matrix([[.1, .2], [.2, 1.3]]);
Ap := LUDecomposition(Cov, 'method' = 'Cholesky');

Cov = Ap.Transpose(Ap);
Ap = Transpose(Ap)

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