TY - JOUR
AU - Taber, Henry
AB - 1896.] On Stieltjes' Theorem. 613 On a Twofold Generalization of Stieltjes' Theorem. By HENRY TABER, Worcester, Mass. Received June 8th, 1896. Read June 11th, 1896. In a paper " Sur une propriete des determinants sym6triques gauche " which appeared in Volume XVII., Second Series (1892) of the Memoires de la Societe Roy ale des Sciences de Liege, M. Francois Deruyts gave the following very interesting theorem:— If the minors of order 2k of a skew symmetric determinant are all zero, the minors of order 2k— 1 are all zero also. As an immediate consequence of this theorem follow certain theorems of some interest relating to orthogonal substitutions, among which is included a two-fold generalization of Stieltjes' theorem. Let the transformation A denned by the system of equations x' = a iX + a x +...+a x (r = 1, 2, ... n) r r 1 r2 a rn n be any orthogonal substitution in n variables. Let A denote the i+i) linear transformation denned by the system of equations a>r — a x +... + a . x . + &„—p) x +a x + + ...+a x ri l r>r 1 r i r rtr+1 r l m 
TI - On a Twofold Generalization of Stieltjes' Theorem
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s1-27.1.613
DA - 1895-11-01
UR - https://www.deepdyve.com/lp/wiley/on-a-twofold-generalization-of-stieltjes-theorem-GuZBckfhFT
SP - 613
EP - 621
VL - s1-27
IS - 1
DP - DeepDyve
ER -