search for: lambda_k

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2004 Jun 07
2
MCLUST Covariance Parameterization.
...Raftery. My problem is trying to figure out how the (model) identifier (e.g, EII, VII, VVI, etc.) relates to the covariance matrix. The parameterization of the covariance matrix makes use of the method of decomposition in Banfield and Rraftery (1993) and Fraley and Raftery (2002) where Sigma_k = lambda_k*D_k*A_k*D_k^' where Sigma_k is the covariance matrix for the kth (k=1,...,G), lambda_k is the kth groups constant of proportionality, D_k is the orthogonal matrix of eigenvectors for the kth group, and A_k is a diagonal matrix whose elements are proportional to the eigenvalues. The parameteri...
2004 Dec 03
3
Computing the minimal polynomial or, at least, its degree
Hi, I would like to know whether there exist algorithms to compute the coefficients or, at least, the degree of the minimal polynomial of a square matrix A (over the field of complex numbers)? I don't know whether this would require symbolic computation. If not, has any of the algorithms been implemented in R? Thanks very much, Ravi. P.S. Just for the sake of completeness, a