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In chapter 8 of "Matrix Algebra from a Statistician's Perspective", the author describes the construction of an orthogonal matrix, the first row of which is proportional to some row vector of non-zero entries. Try as I might, I cannot find anything related to this matrix, only the so-called Helmert transformation on Wikipedia.

Does anybody know in which areas of statistics such matrices are encountered?

user143074
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  • If I recall correctly they can be used to prove that $\bar{X}$ and $S^2$ from iid normal data are independent – Taylor Feb 19 '17 at 14:53
  • I describe one use of Helmert matrices at http://stats.stackexchange.com/a/259223/919 (and reference the same text you do). A much more common and well-known use is in constructing [orthogonal contrasts](http://stats.stackexchange.com/search?q=orthogonal+contrast+helmert). The link identifies many posts on our site concerning this use of Helmert matrices--perhaps one or more therefore directly answer your question? – whuber Feb 19 '17 at 15:10

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