2010 Determinants 



Determinants, theory, origin and develop- 

 ment. Studnicka, F. J. Casopis 5 (* 1876) 

 1-, 88-, 193-, 279-. 



t ) third fundamental proposition, new 

 method of deduction. Studnicka, F. J. 

 Casopis 17 (1888) 193- ; Fschr. Mth. (1888) 

 143. 



of 3rd order, note. Tait, P. G. [1866] 

 Edinb. B. S. P. 6 (1869) 59-. 



4th order, development. Guimaraes, R. 



As. Fr. C. K. (1897) (Pt. 2) 129-. 



3 ; 4 and 5 rows, rules for their calcula- 

 tion by inspection. Teixeira, J. P. G. 

 Teix. J. Sc. 11 (1892) 88-; Fschr. Mth. 

 (1392) 141. 



with triple indices, product expressed as one 

 ordinary determinant. Gassparis, A. de. Rm. 

 R. Ac. Line. T. 3 (1379) 44-. 



and m indices, theorems. Gasparis, 



A. de. Nap. Rd. 7 (1368) 118-. 

 vector constituents. Chapman, C. H. 



J. H. Un. Cir. [9 (1889-90)] 77. 

 Determination of four functions to satisfy a 



certain equation. Vivanti, G. Palermo Cir. 



Mt. Rd. 6 (1892) 100-. 

 Dialytic determinant, evaluation of a certain. 



Taylor, W. W. [1895] L. Mfch. S. P. 27 



(1396) 60-. 



Discriminating symmetrical determinant. Syl- 

 vester, J. J. Crelle J. Mth. 88 (1380) 6-. 

 Distances between points, equation connecting 



mutual. Muir, T. Edinb. Mth. S. P. 3 



(1885) 34-. 

 , relations. Brioschi, F. N. A. Mth. 



14 (1855) 172-. 

 Double series, two, arising from number of 



terms in determinants. Dickson, J. D. H. 



L. Mth. S. P. 10 (1878-79) 120- . 

 Doubly orthosymmetrical determinants. Weih- 



rauch, K. Z. Mth. Ps. 26 (1381) 64-, 



132-. 



skew determinants. Sylvester, J. J. C. R. 

 89 (1879) 24-. 



Equation for max. and min. of ?i-ary quadric. 

 Gravelaar, N. L. W. A. N. Arch. Wisk. 4 

 (*1878) 113-. 



Equations, symmetrical linear, with indeter- 

 minate coefficients, solution by determinants. 

 Stockwell, J. N. Gould As. J. 6 (1361) 

 145-. 



Factorisation of characteristic equation of in- 

 duced substitutions. Rados, (?. Mth. Termt. 

 Ets. 17 (1899) 66-; Mth. Nt. B. Ung. 17 

 (1901) 248-. 



Factors of a special form of determinant. 

 Glaisher, J. W. L. QJ. Mth. 15 (1878) 

 347-. 



Formula of Lagrange generalised by Cauchy. 

 Barbier, E. C. R. 96 (1383) 1345-. 



Liouville's. Lucas, F. C. R. 70 (1370) 



1167-. 



Lucas, connecting n quantities and their 



sum, proof. Albeggiani, M. G. Mt. 13 

 (1875) 107-. 



Formulas, fundamental, of spherical trigono- 

 metry derived from theorem in determinants. 

 Studnicka, F. J. Prag Sb. (1375) 1-. 



Determinants 2010 



Formulae relative to polar operations. Capelli, 



A. G. Mt. 32 (1894) 376-. 

 Functional determinant, property. Brioschi, F. 



QJ. Mth. 1 (1857) 365-. 



determinants. Jacobi, C. G. J. Crelle J. 

 22 (1341) 319-. 



. Combescure, E. Par. EC. Norm. A. 4 



(1367) 93-. 

 . Casorati, F. [1874] Mil. I. Lomb. 



Mm. 13 (1377) 181 -. 

 . Faa de Bruno, F. Mth. A. 18 (1881) 



280-. 

 . Kraus, L. Wien Ak. Sb. 90 (1885) 



(Ab. 2) 813-. 

 _ __. Torelli, G. Palermo Cir. Mt. Rd. 



7 (1893) 75-. 

 , application. Trzaska, W. Par. T. 



Nauk Sc. Pam. 1 (*1871) 113- ; Bll. Sc. Mth. 



As. 6 (*1874) 153. 

 , elementary proof of theorem. Nanson, 



E. J. [1877] Mess. Mth. 7 (1878) 120-. 

 and Jacobian matrices. Giordano, G. 



G. Mt. 38 (1900) 210-. 

 , property. Clebsch, R. F. A. Crelle 



J. 69 (1868) 355-; 70 (1869) 175-. 

 , and application to implicit functions. 



Gilbert, P. [1869] Brux. Ac. Sc. Mm. 38 



(1871) 12 pp. 

 , rational. Mansion, P. [1879] Mess. 



Mth. 9 (1880) 30-. 

 , , generalisation. Mertens, F. Krk. 



Ak. (Mt.-Prz.) Pam. 16 (1889) 60-; Fschr. 



Mth. (1889) 151-. 

 , _, theorems. Anglin, A. H. [1886] 



Ir. Ac. P. 4 (1884-88) 645-. 

 , theorem (Hesse). Zmurko, W. Par. 



T. Nauk Sc. Pam. 1 (*1871) 89-. 

 , (Jacobi). Donkin, W. F. Camb. 



and Dubl. Mth. J. 9 (1854) 161-. 



t theory. Neumann, C. Mth. A. 1 

 (1869) 208-. 



Functions analogous to determinants. Dah- 



lander, G. R. Stockh. Ofv. 20 (1863) 295-. 

 Fundamental operations of arithmetic, genera- 

 lisation. Schapira, H. D. Nf. Tbl. (*1882) 



128-. 

 Geometrical series of 2nd order. Hochheim, A. 



Magdeb. Nt. Vr. Jbr. u. Ab. (1886) 127- ; 



(1887) 25-. 

 Goniometrical determinants, some. Weihrauch, 



K. Z. Mth. Ps. 36 (1891) 71-. 

 Grassmann's method applied to prove theorems 



in determinants. Miiller, E. Z. Mth. Ps. 



44 (1899) 28-. 

 Harmonic determinant, condition for equal 



roots. Tarleton, F. A. [1887] Ir. Ac. P. 1 



(1889-91) 10-. 

 Hesse, theorem (Hessian determinant). Gor- 



dan, P. Erlang. Ps. Md. S. Sb. 8 (1876) 89-. 

 Hessian. Segre, C. Rm. R. Ac. Line. Rd. 



4 (1895) (Sem. 2) 143-. 

 , application of exponential polygon. Eddy, 



H. T. Des Moines Anal. 2 (1875) 104-. 

 , change of independent variables in a. 



Nanson, F. J. Mess. Mth. 25 (1896) 139-. 



determinant. Voss, A. Mth. A. 30 (1887) 

 418-. 



133 



