Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all permutations, the number of transpositions necessary determining the sign to be affixed to the member.
From the theorem given above for the expansion of a determinant as a sum of products of pairs of corresponding determinants it will be plain that the product of A= (a ll, a22, ï¿½ï¿½ï¿½ ann) and D = (b21, b 22, b nn) may be written as a determinant of order 2n, viz.
Anibll +an2b12+ï¿½ ï¿½ï¿½ +annbin a11b21+a12b22+ï¿½ï¿½ï¿½ +alnb2n, a21b21+a22b22+ï¿½ï¿½ï¿½ +a2nb2n, ï¿½ ï¿½ ï¿½ ani b21 + a n2 b 22 + ï¿½ ï¿½ ï¿½ +annb2n alib31+a12b32+ï¿½ï¿½ï¿½+ainb3n, a21b31+a22b32+ï¿½ï¿½ï¿½+a2nb3n, .ï¿½.a n lb 31 + a n2 b 32+ ï¿½ï¿½ï¿½ +annb2n a ll b nl + a 12 b n2+ ï¿½ï¿½ï¿½ + a ln b nn, a21bn1+a22bn2+ï¿½-ï¿½+a2nbnn, ï¿½ ï¿½ ï¿½ ani b nl + a n2 b n2 +ï¿½ ï¿½ ï¿½ +annbnn and all the elements of D become zero.
In particular the square of a determinant is a deter minant of the same order (b 11 b 22 b 33 ...b nn) such that bik = b ki; it is for this reason termed symmetrical.
The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 ï¿½ï¿½ï¿½ A nn).
If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
Draw NR the same multiple of Nn and upwards.
Schoma.nn and of G.
With urea it gives " /CH NN quinazolone I, and with mandelic nitrile and its H /C0 homologues it forms oxazole derivatives (S.
Meyer, A nn., 1870, 156, p. 274).
The diagonal telescope nn is provided with cross hairs, and is used fcr the final centring of the instrument over an object.
A set of stirring blades carried in the frame (b b), and driven by gearing, NN,, ï¿½,, .
Some phonetic characteristics of the dialect may be regarded as quite certain; (I) the change of the original short o to a (as in the last syllable of the genitive kalatoras); (2) of final -m to -n (as in g ran); (3) of -ni- -ti- -si- respectively to -nn- -to- and -ss- as in dazohonnes " Dasonius," dazohonnihi " Dasonii"; dazetOes, gen.
One important fact should m nn 23yz FIG.
Nn, Nemacaulus or virgular tube.
Conceiving the line NN' to be that of the nodes at any time, and the earth and lunar orbit to be moving in the direction of the straight arrows, the earth will be on one side of the ecliptic from M2 to M5, and on the other side from M6 to M 1, intersecting it at the nodes.
Nj and nn give n mouillhe (ny in both old and modern spelling: senyor.
Nn, mn, nj, and sometimes to initial n: ao (a nn u m), dano (d a m n u m), nudo (n 0 d u m).