2010 Determinants 



Linear substitutions applied to theory of groups. 



Laurent, H. N. A. Mth. 16 (1897) 149-. 

 , reduction. Jordan, C. Par. EC. Pol. 



J. 29 ( = Cah. 48) (1880) 15 1-. 

 transformations of quadratic form. Boole, 



G. Camb. Mth. J. 4 (1845) 167-. 

 , general theory. Boole, G. Camb. Mth. 



J. 3 (1843) 1-, 106-. 

 , points in theory. Philippot, I. H. Liege 



S. Sc. Mm. 20 (1898) No. 9, 14 pp. 

 Eational reversible substitutions. Kraus, L. 



Prag Sb. (1882) 338-; (1883) (Mth.-Vortr.) 



187-. 

 Representation of binary homographies by 



points of space, with application to spherical 



rotations. Stephanos, C. Mth. A. 22 (1883) 



299-. 

 Salmon's "Higher Algebra." Bellavitis, G. 



Yen. Mm. I. 9 (1860) 237-. 

 Space, division by linear transformation groups. 



Dyck, W. Leip. Mth. Ps. B. 35 (1883) 61-. 

 Theorem on two contrary substitutions. Lip- 



schitz, E. 0. S. Am. J. Mth. 1 (1878) 336-. 

 . Sylvester, J. J. Am. J. Mth. 



1 (1878) 341-. 

 Umbral notation. Barley, (Rev.) E. B. A. 



Bp. (1887) 600-. 



2010 Determinants. 



Adjoint minors. Landsberg, G. Crelle J. Mth. 



109 (1892) 225-. 

 Adjugate determinant. Huir, T. [1894] Edinb. 



B. S. P. 20 (1895) 323-. 

 Algebraic determinant, a special. Weihrauch, 



K. Z. Mth. Ps. 36 (1891) 34-. 



determinants, reduction. Eussell, W. H. L. 

 E. A. Bp. (1885) 910-. 



expressions unaltered by certain substitu- 

 tions. Glaisher, J. W. L. [1880] Mess. 

 Mth. 10 (1861) 60-. 



reversibility, new theorem. Andre, D. Par. 

 S. Mth. Bll. 24 (1896) 136-. 



Alternant of even number of letters, Jacobi's 



form. Muir, T. [1900] Edinb. B. S. P. 23 



(1902) 133- . 

 , multiplication by symmetric function. 



Muir, T. [1899] Edinb. B. S. P. 22 (1900) 



539-. 

 Alternants. Muir, T. [1879] Edinb. B. S. P. 



10 (1880) 102-. 

 . Starkov. A. N. Es. S. Nt. Mm. (Mth.) 



10 (1889) 143-. 



. Muth, P. Crelle J. Mth. 122 (1900) 89-. 

 , a class of. Loria, G. Prag Sb. (1897) 



(Mth.-Nt.) No. 57, 13 pp. 

 , constant multiples of the difference product 



of the variables. Anglin, . [1888] Edinb. 



B. S. P. 15 (1889) 468-. 



and elliptic functions, identities connected 

 with. Muir, T. [1900] Edinb. B. S. T. 40 

 (1905) 187-. 



, history. Muir, T. [1900] Edinb. B. S. P. 



23 (1902) 93-. 

 , summation of certain series. Anglin, A. H. 



[1887] Edinb. E. S. P. 14 (1888) 194-. 



Determinants 2010 



Alternants, theorems connected with. Anglin, 



A. H. [1886-88] Edinb. E. S. P. 13 (1886) 

 823- ; 15 (1889) 381-. 



of the 3rd order, a formula of reduction 

 for. Johnson, W. W. Am. J. Mth. 7 (1885) 

 347-. 



, geometrical representation. 

 Johnson, W. W. QJ. Mth. 21 (1886) 2 17-. 



4th order, calculation of co-factors. 

 Johnson, W. W. Am. J. Mth. 7 (1885) 380-. 



Alternating functions. Cauchy, A. L. [1812] 



Par. EC. Pol. J. 10 (1815) (17 e cah.) 29-. 

 . Jacobi, C. G. J. Crelle J. 22 (1841) 



360-. 

 and applications. Cauchy, A. L. C. E. 



10 (1840) 178- ; 13 (1841) 939-. 

 , a class of. Muir, T. [1887] Edinb. B. 



S. T. 33 (1888) 309-. 



of n variables. Scott, E. F. [1881] 

 Mess. Mth. 11 (1882) 98-. 



, reduction to alternants. Johnson, W. W. 



Am. J. Mth. 7 (1885) 345-. 

 used in elimination. Cauchy, A. L. C. 



B. 12 (1841) 414-. 



sums. Cauchy, A. L. C. B. 13 (1841) 939-. 

 Arithmetical determinant, value of certain. 



Smith, H. J. S. L. Mth. S. P. 7 (1875-76) 

 208-. 



determinants, certain. Cesdro, E. G. Mt. 

 23 (1885) 182-, 367 ; Em. B. Ac. Line. Ed. 

 1 (1885) 709-, 711-. 



of higher dimension. Gegenbauer, L. 



Wien Ak. Sb. 101 (1892) (Ab. 2 a) 425-. 



Bernoullian number expressed as a combina- 

 tional determinant. Dupuis, N. F. Cn. B. 

 S. P. & T. 7 (1890) (Sect. 3) 20-. 



Bernoulli's and Euler's numbers, representa- 

 tion by determinants. Sachse, A. Arch. 

 Mth. Ps. 68 (1882) 427-. 



Bibliography. Muir, T. QJ. Mth. 18 (1882) 

 110- ; 21 (1886) 299-. 



Binary determinants. Brioschi, F. Crelle J. 

 52 (1856) 133-. 



Bipartite functions. Muir, T. Edinb. E. S. 

 T. 32 (1887) 461-. 



and determinants, new relations between. 



Muir, T. L. Mth. S. P. 16 (1884-85) 276-. 



Bordered determinants. Le Paige, C. M. M. 

 H. H. Par. S. Mth. Bll. 8 (1880) 128-. 



. Arnaldi, M. G. Mt. 34 (1896) 209-. 



skew determinant. Muir, T. Edinb. E. S. 

 P. 21 (1897) 342-. 



symmetric determinant, Cayley's theorem. 



Muir, T. QJ. Mth. 18 (1882) 46-. 

 Cauchy 's determinant and aleph functions. 



Crocchi, L. [1878] G. Mt. 17 (1879) 2 18-, 



380. 

 Circle touching three circles on a sphere. 



Trzaska, W. Par. T. Nauk. Sc. Pam. 1 



(*1871) 123- ; Bll. Sc. Mth. As. 6 (*1874) 



153. 

 Circulant determinants. Torelli, G. Nap. Ed. 



21 (1882) 83-. 

 Circulants. Studnicka, F. J. Mh. Mth. Ps. 



10 (1899) 193-. 

 , detached theorems on. Muir, T. Edinb. 



E. S. T. 32 (1887) 639-. 



127 



