文档介绍：PrefaceThe last treatise on the theory of determinants, by T. Muir, revised andenlarged by . Metzler, was published by Dover Publications Inc. in1960. It is an unabridged and corrected republication of the edition origi-nally published by Longman, Green and Co. in 1933 and contains a prefaceby Metzler dated 1928. The Table of Contents of this treatise is given inAppendix small number of other books devoted entirely to determinants havebeen published in English, but they contain little if anything of importancethat was not known to Muir and Metzler. A few have appeared in Germanand Japanese. In contrast, the shelves of every mathematics library groanunder the weight of books on linear algebra, some of which contain shortchapters on determinants but usually only on those aspects of the subjectwhich are applicable to the chapters on matrices. There appears to be tacitagreement among authorities on linear algebra that determinant theory isimportant only as a branch of matrix theory. In sections devoted entirelyto the establishment of a determinantal relation, many authors de?ne adeterminant by ?rst de?ning a matrixMand then adding the words: “LetdetMbe the determinant of the matrixM” as though determinants haveno separate existence. This belief has no basis in history. The origins ofdeterminants can be traced back to Leibniz (1646–1716) and their prop-erties were developed by Vandermonde (1735–1796), Laplace (1749–1827),Cauchy (1789–1857) and Jacobi (1804–1851) whereas matrices were not in-troduced until the year of Cauchy’s death, by Cayley (1821–1895). In thisbook, most determinants are de?ned PrefaceIt may well be perfectly legitimate to regard determinant theory as abranch of matrix theory, but it is such a large branch and has such largeand independent roots, like a branch of a banyan tree, that it is capableof leading an independent life. Chemistry is a branch of physics, but itis su?ciently extensive and profound to deserve its traditional r