A Treatise on the Theory of Invariants

The object of this book is, first, to present in a volume of medium size thefundamental principles and processes and a few of the multitudinous applicationsof invariant theory, with emphasis upon both the nonsymbolical andthe symbolical method. Secondly, opportunity has been taken to emphasize alogical development of this theory as a whole, and to amalgamate methods ofEnglish mathematicians of the latter part of the nineteenth century{Boole, Cayley, Sylvester, and their contemporaries{and methods of the continental school, associated with the names of Aronhold, Clebsch, Gordan, and Hermite.The original memoirs on the subject, comprising an exceedingly large andclassical division of pure mathematics, have been consulted extensively. I havedeemed it expedient, however, to give only a few references in the text. Thestudent in the subject is fortunate in having at his command two large andmeritorious bibliographical reports which give historical references with muchgreater completeness than would be possible in footnotes in a book. These arethe article \Invariantentheorie" in the \Enzyklopadie der mathematischen Wissenschaften"(I B 2), and W. Fr. Meyer's \Bericht uber den gegenwartigen Standder Invarianten-theorie" in the \Jahresbericht der deutschen Mathematiker-Vereinigung" for 1890-189