도지슨 응축

개요

• 행렬식을 계산하는 방법의 하나
• nxn 행렬의 행렬식을 2x2 행렬의 행렬식을 반복적으로 계산하여 얻음

예

\(n=3\)의 경우

\[ \begin{vmatrix} p & q & r \\ s & t & u \\ v & w & x \end{vmatrix} = \begin{vmatrix} \begin{vmatrix} p & q \\ s & t \end{vmatrix} & \begin{vmatrix} q & r \\ t & u \end{vmatrix} \\ \begin{vmatrix} s & t \\ v & w \end{vmatrix} & \begin{vmatrix} t & u \\ w & x \end{vmatrix} \end{vmatrix} = \begin{vmatrix} -q s+p t & -r t+q u \\ -t v+s w & -u w+t x \end{vmatrix} = -r t v+q u v+r s w-p u w-q s x+p t x \]

\[ \begin{vmatrix} 5 & 1 & 2 \\ 6 & 1 & 3 \\ 7 & 5 & 4 \\ \end{vmatrix}= \begin{vmatrix} -1 & 1 \\ 23 & -11 \\ \end{vmatrix}=-12 \]

\(n=4\)인 경우

\[ \begin{vmatrix} 2 & 1 & -1 & -3 \\ 1 & -2 & 3 & 0 \\ 3 & 1 & 2 & -1 \\ 0 & -2 & 3 & 1 \\ \end{vmatrix}= \begin{vmatrix} -5 & 1 & 9 \\ 7 & -7 & -3 \\ -6 & 7 & 5 \\ \end{vmatrix}= \begin{vmatrix} -14 & 20 \\ 7 & -7 \\ \end{vmatrix} =6 \]

메모

• 1986 Robbins-Rumsey lambda determinant
• Dodgson’s condensation method for computing determinants has led to the notion of alternating sign matrices and to their remarkable combinatorics. These topics have connections with the 6-vertex model in physics and statistical mechanics and with much recent work on graphical condensation, group characters, and a whole lot more.

관련된 항목들

• 행렬식
• 데스나노-자코비 항등식

매스매티카 파일 및 계산 리소스

• https://docs.google.com/leaf?id=0B8XXo8Tve1cxYzMyMTI2ZGEtNmZlNi00ZWMyLWFkODctMWQzZjc0OGU3NjVm&sort=name&layout=list&num=50

수학용어번역

• condense - 대한수학회 수학용어집
• Dodgson - 발음사전 Forvo

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Dodgson_condensation

리뷰논문, 에세이, 강의노트

• Hone, Andrew N. W. 2006. “Dodgson Condensation, Alternating Signs and Square Ice.” Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 364 (1849): 3183–3198. doi:10.1098/rsta.2006.1887.
• Abeles, Francine F. 2008. “Dodgson Condensation: The Historical and Mathematical Development of an Experimental Method.” Linear Algebra and Its Applications 429 (2-3): 429–438. doi:10.1016/j.laa.2007.11.022.
• Lewis Carroll and His Telescoping Determinants

관련논문

• Berliner, Adam, and Richard A. Brualdi. 2008. “A Combinatorial Proof of the Dodgson/Muir Determinantal Identity.” International Journal of Information & Systems Sciences 4 (1): 1–7.
• Zeilberger, Doron. 1997. “Dodgson’s Determinant-Evaluation Rule Proved by Two-Timing Men and Women.” Electronic Journal of Combinatorics 4 (2): Research Paper 22, approx. 2 pp. (electronic).

메타데이터

위키데이터

• ID : Q4230490

Spacy 패턴 목록

• [{'LOWER': 'dodgson'}, {'LEMMA': 'condensation'}]