2030 



Linear Substitutions 



2030 



Integral linear substitutions not given by alge- 

 braical congruences. Pick, G. Mth. A. 28 

 (1887) 119-. 



Invariants of orthogonal substitutions (regarded 

 as rotations). Schlafli, L. [1865] Crelle J. 

 65 (1866) 185-. 



Inverse orthogonal matrices. Sylvester, J. J. 

 Ph. Mg. 34 (1867) 461-. 



Kummer's configuration, and orthogonal sub- 

 stitutions. Study, E. Leip. Mth. Ps. B. 

 44 (1892) 122-. 



Linear orthogonal substitutions, special case. 

 Stern, M. A. Crelle J. 67 (1867) 293-. 



substitutions. Polignac, C. de. Par. S. 

 Mth. Bll. 4 (1876) 120- ; 5 (1877) 69-. 



. Poincare, H. C. E. 98 (1884) 349-. 



. Picard, E. C. E. 98 (1884) 416-. 



. Burnside, W. Mess. Mth. 22 " 



190-. 

 , certain. Deruyts, J. Brux. Ac. Bll. 



24 (1892) 102-. 

 , a property. Burnside, W. Mess. Mth. 



20 (1891) 163-. 



of a single variable with periodic 

 coefficients. Ocagne, M. d'. Par. S. Mth. 

 Bll. 19 (1891) 37-. 



, special groups of. Fricke, R. Mth. A. 



38 (1891) 50-, 461-. 



, theory. Netto, E. Acta Mth. 17 (1893) 



265-. 



, . Loeicy, A. Mth. A. 48 (1897) 97-; 



49 (1897) 448-. 



, , new. Laurent, H. N. A. Mth. 15 



(1896) 345-. 



by which a quadratic ternary form re- 

 produces itself. Tannery, J. Bll. Sc. Mth. 

 As. 11 (1876) 221-. 



transformations. Cayley, A. Camb. Mth. 

 J. 4 (1845) 193- ; Camb. and Dubl. Mth. J. 

 1 (1846) 104-. 



, some properties. Deruyts, J. Brux. 

 Ac. Bll. 16 (1888) 576-. 



Orthogonal and Boolian invariant systems, 

 . symbolism for. MacMahon, (Maj.) P. A. 



B. A. Ep. (1900) 647. 

 , related, substitutions. Igel, B. [1877] 



Wien Ak. D. 39 (1879) (Ab. 2) 29-. 



substitution, properties of coefficients. Bar- 

 delli, G. Mil. I. Lomb. Ed. 9 (1876) 167-. 



substitutions. Grunert, J. A. Arch. Mth. 

 Ps. 44 (1865) 478-. 



. Gundelftnger, S. Crelle J. Mth. 99 



(1886) 147-. 



. Netto, E. Acta Mth. 9 (1887) 295-. 



. Catalan, E. As. Fr. C. E. (1893) 



(Pt. 2) 19-. 

 . Taber, H. N. Y. Mth. S. Bll. 3 (1894) 



251-. 

 . Rados, G. Mth. Termt. Ets. 18 (1900) 



128- ; Mth. Nt. B. Ung. 18 (1903) 231-. 

 , conditions among coefficients. Rados, G. 



Mth. Termt. Ets. 16 (1898) 123- ; Mth. Nt. 



B. Ung. 16 (1899) 236-. 

 with determinant ( - 1). Weill, G. Par. 



EC. Norm. A. 11 (1894) 23-. 

 , equation connected with. Borsch, A. 



Z. Mth. Ps. 24 (1879) 391-. 



Orthogonal substitutions in involution. Prym, 



F. Gott. Ab. 38 (1892) (Mth.) 42 pp. 

 , parametric expression of coefficients. 



Hunyady, J. Mag. Tud. Ak. Etk. (Mth.) 



14 (1892) No. 2, 43 pp., No. 3, 14 pp.; Mth. 



Nt. B. Ung. 7 (1890) 233-. 

 and regular divisions of space. Goursat f 



E. C. E. 106 (1888) 1786- ; Par. EC. Norm. 



A. 6 (1889) 9-. 

 (single alternate substitution). Taber, H. 



Am. J. Mth. 16 (1894) 123-. 

 , theory. Voss, A. E. Mth. A. 13 (1878) 



320-. 

 , . Rados, G. Mth. Termt. Ets. 10 



(1892) 16-; Mth. Nt. B. Ung. 10 (1893) 95-. 



system in parallel arrangement. Voss, A. 

 Mth. A. 24 (1884) 48-. 



systems. Kronecker, L. Berl. Ak. Sb. 

 (1890) 525-, 601-, 691-, 873-, 1063-. 



Powers and roots of linear substitutions. Syl- 

 vester, J.J. C. E. 94 (1882) 55-. 



Quadratic form, automorphic transformation. 

 Rosanes, J. Crelle J. Mth. 80 (1875) 52-. 



, transformations. Jordan, C. Liouv. 



J. Mth. 4 (1888) 349-. 



, . Loewy, A. Ac. Nt. C. N. Acta 



65 (1896) 1-. 



. , orthogonal transformation to sum of 

 squares. Kneser, A. Arch. Mth. Ps. 15 

 (1897) 225-. 



, reduction. Timerding, H. E. Crelle J. 



Mth. 122 (1900) 172-. 

 , to squares : equation | a^k + S \ = 0. 



Walecki, . N. A. Mth. 1 (1882) 401-, 



556-. 

 , transformation. Enneper, A. Z. Mth. 



Ps. 9 (1864) 358-. 



, to sum of squares. Hesse, L. 0. 

 Crelle J. 45 (1853) 93-; 57 (1860) 175-. 



, . Gundelfinger, S. [1880] 



Crelle J. Mth. 91 (1881) 221-. 

 , . Zajaczkowski, W. (xn) 



[1883] Krk. Ak. (Mt.-Prz.) Pam. 9 (1884) 1- ; 



Fschr. Mth. (1884) 165-. 

 , . . Presle, de. Par. S. 



Mth. Bll. 14 (1886) 98-. 



, , Gauss's method. 

 Somoff, J. St. Pet. Ac. Sc. Bll. 18 (1873) 

 442-. 



forms and the discriminantal equation. 

 Laurent, H. N. A. Mth. 10 (1891) 60S-. 



, reduction to least number of terms, 

 Jacobi, C. G. J. Berl. B. (1848) 414-. 



, and transformation. Jordan, C. 

 Liouv. J. Mth. 19 (1874) 397-. 



, removal of product terms from two. 

 Jacobi, C. G. J. Crelle J. 12 (1834) 1-. 



, simultaneous transformation. Cayley, A . 



Camb. and Dubl. Mth. J. 4 (1849) 47-; QJ. 



Mth. 2 (1858) 192-. 

 , . Siacci, F. Tor. At. Ac. Sc. 



7 (1871-72) 758-. 

 , theory. Jamet, V. Mars. Fac. Sc. A. 



10 (1900) Fasc. 5, 18 pp. 

 , transformation. Smith, Arch. Camb. 



Mth. J. 1 (1839) 272-. 

 , . Cayley, A. Crelle J. 50 (1855) 277-. 



141 



