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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 17개는 보이지 않습니다) | |||
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| − | + | ==개요== | |
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* 행렬식을 계산하는 방법의 하나 | * 행렬식을 계산하는 방법의 하나 | ||
| + | * nxn 행렬의 행렬식을 2x2 행렬의 행렬식을 반복적으로 계산하여 얻음 | ||
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| − | + | ==예== | |
| + | ===<math>n=3</math>의 경우=== | ||
| + | :<math> | ||
| + | \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 | ||
| + | </math> | ||
| − | + | :<math> | |
| + | \begin{vmatrix} | ||
| + | 5 & 1 & 2 \\ | ||
| + | 6 & 1 & 3 \\ | ||
| + | 7 & 5 & 4 \\ | ||
| + | \end{vmatrix}= | ||
| + | \begin{vmatrix} | ||
| + | -1 & 1 \\ | ||
| + | 23 & -11 \\ | ||
| + | \end{vmatrix}=-12 | ||
| + | </math> | ||
| + | |||
| + | ===<math>n=4</math>인 경우=== | ||
| + | :<math> | ||
| + | \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 | ||
| + | </math> | ||
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| − | + | ==메모== | |
| − | + | * 1986 Robbins-Rumsey lambda determinant | |
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* 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. | * 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. | ||
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| − | + | ==관련된 항목들== | |
| + | * [[행렬식]] | ||
| + | * [[데스나노-자코비 항등식]] | ||
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| − | + | ==매스매티카 파일 및 계산 리소스== | |
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* https://docs.google.com/leaf?id=0B8XXo8Tve1cxYzMyMTI2ZGEtNmZlNi00ZWMyLWFkODctMWQzZjc0OGU3NjVm&sort=name&layout=list&num=50 | * https://docs.google.com/leaf?id=0B8XXo8Tve1cxYzMyMTI2ZGEtNmZlNi00ZWMyLWFkODctMWQzZjc0OGU3NjVm&sort=name&layout=list&num=50 | ||
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| − | + | ==수학용어번역== | |
| + | * {{학술용어집|url=condense}} | ||
| + | * {{forvo|url=Dodgson}} | ||
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| − | + | ==사전 형태의 자료== | |
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/Dodgson_condensation | * http://en.wikipedia.org/wiki/Dodgson_condensation | ||
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| − | * | + | ==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. |
| − | * http:// | + | * 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. |
| + | * [http://thalesandfriends.org/wp-content/uploads/2012/03/Telescoping.pdf Lewis Carroll and His Telescoping Determinants] | ||
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| + | ==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). | ||
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| + | [[분류:선형대수학]] | ||
| − | * | + | ==메타데이터== |
| − | + | ===위키데이터=== | |
| − | * | + | * ID : [https://www.wikidata.org/wiki/Q4230490 Q4230490] |
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'dodgson'}, {'LEMMA': 'condensation'}] | ||
2021년 2월 17일 (수) 04:47 기준 최신판
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
매스매티카 파일 및 계산 리소스
수학용어번역
사전 형태의 자료
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'}]