文章基本信息

标题：Quick Constructions of Non-Trivial Real Symmetric Idempotent Matrices
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作者：Nitis Mukhopadhyay
期刊名称：Sri Lankan Journal of Applied Statistics
印刷版ISSN：1391-4987
电子版ISSN：2424-6271
出版年度：2014
卷号：15
期号：1
页码：57-70
DOI：10.4038/sljastats.v15i1.6794
语种：English
出版社：The Institute of Applied Statistics, Sri Lanka
摘要：In the theory and applications of linear models, idempotent matrices appear frequently. It remains important to construct non-trivial quadratic forms distributed as chi-squares. However, quick and easy methods to explicitly construct such matrices with all non-zero entries are hard to come by. We include two direct methods to explicitly exhibit nxn real symmetric idempotent matrices of rank r with all non-zero entries. Then, we exhibit explicit non-trivial real symmetric idempotent matrices A; B such that AB = O:DOI: http://dx.doi.org/10.4038/sljastats.v15i1.6794
关键词：Chi-square; Design matrix; Inverse matrix; Orthogonal vectors; Projection matrix; Quadratic forms