0850 Matrices 



Matrices, fundamental proposition. Weyr, E. 



Prag Sb. (1884) (Mth.-Nt.) 148- ; Fschr. 



Mth. (1885) 107. 

 , multiplication of, identical relation. 



Kretowski, W. Krk. Ak. (Mt.-Prz.) Bz. 6 



(1893) 151- ; Fschr. Mth. (1893-94) 217. 

 , note. Brill, J. [1895-97] L. Mth. S. P. 



27 (1896) 35-; 28 (1897) 368-. 

 , product of two. Sardi, C. G. Mt. 5 (1867) 



, ' . Janni, V. G. Mt. 11 (1873) 



357-. 

 , . Bonolis, A. G. Mt. 34 (1896) 



375-. 



and quaternions. Elfrinkhof, L. van. N. 

 Arch. Wisk. 1 (1895) 88-; Fschr. Mth. 

 (1893-94) 226-. 



satisfying a certain equation. Brunei, . 

 Bordeaux S. Sc. Mm. 4 (1888) xxii. 



, spherical geometry theorem proved by. 

 Chrystal, G. Edinb. Mth. S. P. 2 (1884) 45-. 



of substitution. Brunei, . Bordeaux 

 S. Sc. Mm. 4 (1888) viii. 



, theorem by Cayley, proof. Forsyth, A. R. 



Mess. Mth. 13 (1884) 139-. 

 , theory. Cayley, A. Phil. Trans. 148 



(1858) 17-; 156 (1866) 25-. 

 , . Buchheim, A. L. Mth. S. P. 16 



(1884-85) 63-. 

 , . Weyr, E. C. B. 100 (1885) 787-; 



Prag Sb. (1887) (Mth.-Nt.) 358-. 

 , . Taber, H. Am. J. Mth. 12 (1890) 



337-. 

 , , identities in. Taber, H. Am. J. Mth. 



13 (1891) 159-. 

 Matrix, a. Ravut, L. N. A. Mth. 17 (1898) 



us-. 



(a, b) , . . ax + b 

 . ', and function _, , 



Mess. Mth. 



(1880) 104-. 



of third order, square root of. Cayley, A. 

 Edinb. B. S. P. 7 (1872) 675-. 



which represents a vector. Chapman, C. H. 

 Am. J. Mth. 13 (1891) 363-. 



Monothetic equations. Sylvester, J. J. C. B. 



99 (1884) 13-. 

 Non-degenerate matrices, Sylvester's theorem. 



Taber, H. Am. Ac. P. 27 (1893) 46-. 

 Notation for matrices, etc. Cayley, A. Crelle 



J. 50 (1855) 277-. 

 Quaternion equation qQ-Qq' = Q. Cayley, A. 



Mess. Mth. 14 (1885) 108-. 



matrix. Wettum, T. B. van. N. Arch. 

 Wisk. 18 (1891) 168- ; Fschr. Mth. (1891) 



. Elfrinkhof, L. van. N. Arch. Wisk. 



19 (1892) 143- ; Fschr. Mth. (1892) 141-. 



symbols, application to matrix. Taber, H. 

 [1890] L. Mth. S. P. 22 (1891) 67-. 



Boots of matrices. Metzler, W. H. Am. J. 



Mth. 14 (1892) 326-. 

 unitary matrices. Sylvester, J. J. C. B. 



94 (1882) 396-. 

 zeroidal matrices. Brunei, G. C. B. 



106 (1888) 467-. 

 Split matrix, properties. Sylvester, J. J. (xn) 



J. H. Un. Cir. [1] (1882) 210-. 



Other Complex Numbers 0860 



Trinomial unilateral quadratic equation in 

 matrices of second order. Sylvester, J. J. 

 QJ. Mth. 20 (1885) 305-. 



Vectors and linear transformations, with physi- 

 cal applications. Carvallo, E. Mh. Mth. 

 Ps. 2 (1891) 177-, 225-, 311-. 



, , note on Carvallo's paper. 



Peano, G. Mh. Mth. Ps. 5 (1894) 136. 



0860 Other special sorts of 

 complex numbers. 



Associative imaginaries. Cayley, A. (xn) J. 

 H. Un. Cir. [1] (1882) 211-. 



Biquaternions. Clifford, W. K. L. Mth. S. 

 P. 4 (1873) 381-. 



, application to plane geometry. Com- 

 bebiac, . Par. S. Mth. Bll. 26 (1898) 

 259-. 



, coplanar, or doubly complex quantities, 

 theory. Seydler, A. J. Prag Sb. (1881) 80-. 



, geometrical interpretation of results. Ha- 

 milton, (Sir) W. R. Ir. Ac. P. 5 T1853) 

 388-. 



, memoir. Buchheim, A. Am. J. Mth. 7 

 (1885) 293-. 



Classes of numbers derived from real numbers 

 by dexter and sinister operations. Burali- 

 Forti, C. Tor. Ac. Sc. At. 29 (1894) 382-. 



Complex functions, generalisation of founda- 

 tions. Scheffers, G. Leip. Mth. Ps. B. 45, 

 (1893) 828-; 46 (1894) 120-. 



numbers extended. Vahlen, T. Konigsb. 

 Schr. 38 (1897) [72]-. 



formed from n principal units. Weier- 

 strass, K. Gott. Nr. (1884) 395-. 



. Schwarz, H. A. Gott. 



Nr. (1884) 516-. 

 . Dedekind, R. Gott. Nr. 



(1885) 141-. 



. Holder, 0. Gott. Nr. 



(1886) 241-. 



. Weyr, E. Bll. Sc. Mth. 



11 (1887) 205-. 

 . Scheffers, G. Leip. 



Mth. Ps. B. 41 (1889) 290-. 

 . Schur, F. Mth. A. 33 



(1889) 49-. 

 . Gegenbauer, L. Mh. 



Mth. Ps. 2 (1891) 429-. 

 . Hilbert, D. Gott. Nr. 



(1896) 179-. 



, general. Dedekind, R. Gott. Nr. 



(1887) 1-. 



and groups of transformations. Study, E. 



Leip. Mth. Ps. B. 41 (1889) 177. 

 of n dimensions. Petersen, J. Gott. Nr. 



(1887) 489-. 

 , real systems. Carton, E. C. B. 124 



(1897) 1296-. 



, systems. Study, E. Gott. Nr. (1889) 



237-. 

 , . Carton, E. C. B. 124 (1897) 



1217-. 

 , of higher. Molten, T. Mth. A. 41 



(1893) 83-; 42 (1893) 308-. 



63 



