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Multivariate Statistical Analysis in the Real and Complex Domains
Multivariate statistical analysis often proves to be a challenging subject for students. The
difficulty arises in part from the reliance on several types of symbols such as subscripts,
superscripts, bars, tildes, bold-face characters, lower- and uppercase Roman and Greek
letters, and so on. However, resorting to such notations is necessary in order to refer to
the various quantities involved such as scalars and matrices either in the real or complex
domain. When the first author began to teach courses in advanced mathematical statistics
and multivariate analysis at McGill University, Canada, and other academic institutions
around the world, he was seeking means of making the study of multivariate analysis
more accessible and enjoyable. He determined that the subject could be made simpler
by treating mathematical and random variables alike, thus avoiding the distinct notation
that is generally utilized to represent random and non-random quantities. Accordingly, all
scalar variables, whether mathematical or random, are denoted by lowercase letters and
all vector/matrix variables are denoted by capital letters, with vectors and matrices being
identically denoted since vectors can be viewed as matrices having a single row or column
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