An application of the modified Leverrier-Faddeev algorithm to the singular value decomposition of block-circulant matrices and the spectral decomposition of symmetric block- circulant matrices
نویسنده
چکیده
The Leverrier-Faddeev algorithm, as modified by Gower (1980), is little-known but is useful for deriving the algebraic, rather than numerical, spectral structure of matrices occurring in statistical methodology. An example is given of deriving explicit forms for the singular value decomposition of any block-circulant matrix and the spectral decomposition of any symmetric block-circulant matrix. Such problems arise in special forms of multiple correspondence analysis.
منابع مشابه
2nd Special issue on matrix computations and statistics
A number of interesting and important ideas have resulted from the relationship between matrix computations and statistics. Well-known examples include the solution of least-squares problems, computation of the singular value decomposition and its generalizations, estimation of principal components, computation of canonical correlations, several cluster analysis algorithms, and the solution of ...
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