# Items tagged with covariancecovariance Tagged Items Feed

### Cholesky Decomposition for a symbolic...

January 30 2013 by Maple

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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...

### Singular covariance matrix

March 21 2012 by Maple

Hi everyone,

I want to create a Gaussian PDF so I need to calculate Determinant(sigma) with sigma the covariance matrix of a gaussian variable.

If we call this variable alpha (which is a 12 dimension vector and represents the noise in a discrete dynamical equation), then sigma_ij=ExpectedValue(alpha_i*alpha_j)-ExpectedValue(alpha_i)*ExpectedValue(alpha_j)

and this is zero most of the time! So the covariance matrix is singular and the determinant is zero.

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