Get An Introduction to Determinants, Being a Chapter from The PDF

By William Snow Burnside, Arthur William Panton

ISBN-10: 1171616937

ISBN-13: 9781171616931

This quantity is made from electronic photos from the Cornell collage Library ancient arithmetic Monographs assortment.

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Additional resources for An Introduction to Determinants, Being a Chapter from The Theory of Equations

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18) " (k i #k2 # •# * *kn + 2 ^ • Thus it follows from (3«10) and (3«18) Z ( t S g! ) * Z (G j) + 2 . 1 9 ) (a) of this proof we now form the corresponding quantities v ( k p )i z(kp ), rp and rp for lows from (3*15), instead of T 1 w i th m » n+2. 20) X 1 , too« 45 For each p e ( l , . . , n + 2 ? 17). Now we proceed to determine the w p 's f°r kp“ i 2 # By (3*15) we have t ^ 4. From the validity of (3*20) and G g € TG it follows by Lemma 2 that the vertices of the subgraph of G^* G 2 gen­ erated by { ( i .

Ku ■ kB ) in this subgraph. ,ku - 1|; we define v( kp ) » « H q e f l i . . ,«. ,«. 16) we can torn the following paths w pf p ■ l , « « « 9m'# in • GgX 'i(kp . l H ( kp t 2 ) ^ ^ . >11) for the parameters d ■ 1, P a i 2 ■ ±3 # and <* a x+ 1 « We may assume (possibly by taking the inverse sequence) that i 2 * k'n holds« Obviously, there is a shortest (k^,k^)-path w » (k'^aic^plTgj««. jKgakJj) in the subgraph of G^ generated by { ^ » • « . 18) " (k i #k2 # •# * *kn + 2 ^ • Thus it follows from (3«10) and (3«18) Z ( t S g!

From the validity of (3*20) and G g € TG it follows by Lemma 2 that the vertices of the subgraph of G^* G 2 gen­ erated by { ( i . j j G V i G ^ G 2 ) : i * i 2 } (this subgraph is isomorphic to G 2 ) can be covered by v ( i 2 ) + lil 2 } n M | paths, so that one of these paths contains J(i 2 * E^G1 * G 2 ^# We choo8e v (*2 ) °* these paths as the w 's for the p*s with k * i 0 ; if i0 € M holds we P p 2 _ Z have one path more, say w * . Forming (for each i with k ^ € Mjthe sequence Ti 4 i2 . 2) i 2 4 i^.

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An Introduction to Determinants, Being a Chapter from The Theory of Equations by William Snow Burnside, Arthur William Panton


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