MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



A;/ is the first minor of the determinant A corresponding to a,-,- and is a de- 

 terminant of order n i. It may be obtained from A by crossing out the row 

 and column which intersect in an, and multiplying by (1 )*+'. 



1.342 



A 



a in A /n = 



f 



f 



1.343 



a 2 A 



is the coefficient of a^aki in the complete expansion of the determinant A. It 

 may be obtained from A, except for sign, by crossing out the rows and columns 

 which intersect in <m and a k i. 



1.344 



The determinant 

 1.345 



A- 



1.346 



1.347 



1.348 If A = o, 



dai 



A 2 



X | a ti I = A 



I A,, | = A-'. 

 is the reciprocal determinant to A. 



dan da k j 



a 2 A 



aA 



a 2 A 



aA aA 



1.350 If fl 



determinant 



1.351 If at j 

 determinant 



aji the determinant is symmetrical. In a symmetrical 



&<*.- A* 



-a a the determinant is a skew determinant. In a skew 



