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This comprehensive text covers both applied and theoretical branches of matrix algebra in the statistical sciences. Self-contained and appropriate for advanced undergraduate and graduate students, it also constitutes a handy reference. High school mathematics and a first course in statistics are the sole prerequisites. Consisting of two interrelated parts, it begins by dealing with the basic structure of vectors and vector spaces. The latter part emphasizes the diverse properties of matrices and their associated linear transformations - and how these, in turn, depend upon results derived from linear vector spaces.