2030 Linear Substitutions 



Quadratic forms, transformation. Trudi, N. 



Nap. Kd. 1 (1862) 113-. 



, . Brioschi, F. G. Mt. 1 (1863) 26-. 



, . Lemonnier, H. [1874] Par. S. 



Mth. Bll. 3 (1875) 48-. 

 , transformations. Kretkmvski, W. (xn) 



Krk. Ak. (Mt.-Prz.) Pam. 7 (1882) 69-. 

 Quadratics, reduction to canonical form. Sardi, 



C. G. Mt. 5 (1867) 35-. 

 Quadric automorphic linear transformation. 



Muir, T. [1897] Edinb. E. S. T. 39 (1900) 



209-. 

 Quaternary quadratic form, automorphic linear 



transformations. Bachmann, . D. Nf. 



Tbl. (*1871) 138-. 

 Eeal linear transformations whose invariant is 



an alternant. Taber, H. Am. Ac. P. 31 



(1896) 336-. 



. a real quadratic form. 

 Taber, H. Am. Ac. P. 32 (1897) 75-. 



orthogonal substitution. Taber, H. Am. 

 Ac. P. 28 (1893) 212-. 



Boots of substitutions. Kirkman, T. P. B. A. 

 Ep. (1860) (pt. 2) 4-; (1861) (pt. 2) 4-. 



Solutions of the equation SX=XS. Voss, A. 

 Munch. Ak. Sb. 26 (1897) 273-. 



Special automorphic groups and quadratic 

 forms. Fricke, R. Mth. A. 39 (1891) 62-. 



Structure of linear groups with quadratic in- 

 variants. Dickson, L. E. L. Mth. S. P. 

 30 (1899) 70-. 



Substitutions permutable inter se. Cauchy, 

 A, L. C. E. 21 (1845) 1188-. 



. , and other systems of substitutions. 



Cauchy, A. L. C. E. 21 (1845) 1238-. 



, product of two. Miller, G. A. Am. J. 



Mth. 22 (1900) 185-. 

 , regular, irregular, and conjugate. Cauchy, 



A. L. C. E. 21 (1845) 835-, 895-, 931-, 



972-, 1025-. 



of six letters. Betti, E. C. E. 63 (1866) 

 878. 



which do not alter value of a function. 

 Cauchy, A. L. C. E. 21 (1845) 1234- . 



of several variables, 



number and form. Cauchy, A. L. C. E. 



21 (1845) 1287-. 

 Ternary substitutions of determinant unity with 



integral coefficients. Burn-side, W. Mess. 



Mth. 24 (1895) 109-. 

 Type of successive linear substitutions. Velt- 



mann, W. Arch. Mth. Ps. 58 (1876) 342-. 



2040 General theory of quantics. 



Absolute invariants of integral linear trans- 

 formation groups. Hurwitz, A. Mth. A. 

 20 (1882) 125-. 



Algebraic forms. Cambescure, E. Par. EC. 

 Norm. A. 1 (1864) 269-. 



in any number of variables. Deruyts, J. 



Brux. Ac. Bll. 15 (1888) 951-. 



, geometrical applications. Le Paige, 

 C. M. M. H. H. [1878] Brux. Mm. Cour. 

 4 C , 42 (1879) (No. 4) 71 pp. 



with Hessian determinant vanishing 

 identically. Noether, M. Erlang. Ps. Md. 

 S. Sb. 8 (1876) 51-. 



Quantics 2040 



Algebraic forms with Hessian determinant 



vanishing identically. Gordan, P. , (& Noether, 



M. Mth. A. 10 (1876) 547-. 

 , invariants of a class. Deruyts, J. Brux. 



Ac. Bll. 23 (1892) 152-. 

 with p variables, theory of. Perrin, R. 



C. E. 104 (1887) 108-. 

 , points in theory. Le Paige, C. M. M. 



H. H. Liege S. Sc. Mm. 9 (1882) (No. 4) 



23pp. 



, principle of classification. Rosanes, J. 

 Crelle J. 76 (1873) 313-. 



, property. Le Paige, C. M. M. H. H. 



Mth. A. 15 (1879) 206- . 



with several series of variables. Le 

 Paige, C. M. M. H. H. C. E. 94 (1882) 

 31-, 69-. 



variables, development by polars. 



Capelli, A. Em. E. Ac. Line. Ed. 7 (1891) 

 (Sem. 1) 161- ; 1 (1892) (Sem. 1) 3-. 



, symbolic representation. Clebsch, A. 

 [1860] Berl. Mb. (1860) 536-; Crelle J. 59 

 (1861) 1-. 



, theorem, with application to binary 

 sextic. Ovidio, E. d'. Palermo Cir. Mt. 

 Ed. 6 (1892) 225-. 



, theory. Sylvester, J. J. C. E. 101 



(1885) 1110-. 

 , , arithmetical. Kronecker, L. Crelle 



J. Mth. 93 (1882) 365-. 

 , , general. Capelli, A. Em. E. Ac. 



Line. Mm. 12 (1882) 529-. 

 , , . Deruyts, J. Liege S. Sc. Mm. 



17 (1892) No. 4, vi + 157 pp. 

 , , new. Sylvester, J. J. C. E. 101 



(1885) 1042-, 1225-, 1461. 

 . , , operations in. Capelli, A. Mth. A. 



37 (1890) 1-. 



Anharmonic ratio and invariant theory of com- 

 plex quantities. Schick, J. [1900] Munch. 



Ak. Sb. 30 (1901) 249-. 

 Associated forms. Kohn, G. Wien Ak. Sb. 



100 (1891) (Ab. 2a) 865-. 

 , general theory. Sylvester, J. J. Camb. 



and Dubl. Mth. J. 6 (1851) 289-. 



, theory of Clebsch and Gordan. Syl- 

 vester, J. J. C. E. 86 (1878) 448-. 



Asyzygetic invariants, extension of a theorem. 



Sylvester, J. J. C. E. 102 (1886) 1430-. 

 Boolian trinomial. Cockle, (Sir) J. [1868] 



Mess. Mth. 5 (1871) 33-. 

 Canonical forms, a certain class. Roberts, R. A. 



[1894] N. Y. Am. Mth. S. Bll. 1 (1895) 



and hyperdeterminants, discovery in. 

 Sylvester, J. J. Ph. Mg. 2 (1851) 391-. 



Chemico-algebraical theory. Frankland, E. 



Am. J. Mth. 1 (1878) 345-. 

 Chemistry and algebra. Sylvester, J. J. Nt. 



17 (1878) 284. 

 Combinants. Betti, E. Tortolini A. 1 (1858) 



344-. 

 _. Gordan, P. [1871] Mth. A. 5 (1872) 



95-. 

 , theory. Stroh, E. Mth. A. 22 (1883) 



393-. 

 Contrariants, a new species of invariants. 



Sylvester, J. J. Ph. Mg. 18 (1884) 374-. 



142 



