Jump to content

Wikipedia:Reference desk/Archives/Mathematics/2013 April 21

From Wikipedia, the free encyclopedia
Mathematics desk
< April 20 << Mar | April | May >> Current desk >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


April 21

[edit]

Matrix estimation

[edit]

In Estimation_of_covariance_matrices#Maximum-likelihood_estimation_for_the_multivariate_normal_distribution, part "using the spectral theorem", why do you need to use the cyclic property of the trace? Why can't you simply define and work form there? All of the working would be exactly the same until "concluding steps" when you simply solve instead. Why split the matrix up into square roots? AnalysisAlgebra (talk) 23:31, 21 April 2013 (UTC)[reply]

I just had a look and didn't see why either, so I've stuck a note on the talk page of the person I think stuck it in as they don't normally do things wrong. Dmcq (talk) 10:49, 23 April 2013 (UTC)[reply]

The matrix is symmetric and its entries are real. And it's non-negative-definite. Hence by the (finite-dimensional) spectral theorem, it can be diagonalized and the diagonal entries are non-negative. Is there a simpler way to show that's it's diagonalizable and the diagonal entries are non-negative? Michael Hardy (talk) 00:50, 25 April 2013 (UTC)[reply]

Thanks, yes the major point here is the product of two symmetric matrices need not be symmetric. Dmcq (talk) 08:33, 25 April 2013 (UTC)[reply]