Matrices, Operators, Null Sets
Originally this chapter was to bridge the discussion of Chapters 6 and 7 on differential forms and the applications in Chapter 9 of differential forms to matrix problems made by James. As the book has grown, material on matrix decompositions, Section 8.1, and an inventory of problems, Section 8.5, has accumulated. This material has been found to be needed by most chapters of the book. Likewise the problems in Chapter 4 on sets of measure zero, although basic, did not cover the needed basics, and Section 8.4 has evolved. The complicated subject of canonical correlations has been segregated into Section 8.2. And under the disguise of being infinite dimensional matrices, Section 8.3 covers some operator theory and some results on Hilbert space valued Gaussian random variables, a subject related to contemporary literature on estimation.
KeywordsGaussian Process Covariance Operator Canonical Correlation Diagonal Entry Trace Class
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