We will present in this chapter some aspects of matrix algebra that are needed in this book. Most results presented here can be found in standard books on matrix algebra. Proofs are provided for those results that are either easily derived or not readily available elsewhere. For readers who have no knowledge of matrix algebra, this chapter is essential for the rest of the book. They may find the one-chapter treatment of matrix algebra in the book by Hildebrand (1954) helpful and informative. For readers who have some knowledge of matrix algebra this chapter can be skimmed or skipped altogether, depending on how familiar they are with the subject. If they want to find the proofs omitted in this chapter or want to devote more time on the subject, the books by Hohn (1965) and Pease (1965) are recommended. The notations employed in this chapter have no relations, in most cases, with the notations adopted in the rest of the book. This point should be kept in mind in referring back to this chapter.
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