"가우스-요르단 소거법"의 두 판 사이의 차이

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==개요==
  
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* 선형대수학의 중요한 알고리즘의 하나
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* 선형연립방정식의 해법, 역행렬의 계산 등에 활용할 수 있다
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==예==
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<math>\left( \begin{array}{ccc}  1 & -3 & 0 \\  -1 & 1 & 5 \\  0 & 1 & 1 \end{array} \right)</math> 에 가우스-조단 소거법을 적용한 경우
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<math>\begin{array}{l}  \left( \begin{array}{ccc}  1 & -3 & 0 \\  -1 & 1 & 5 \\  0 & 1 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & -3 & 0 \\  0 & -2 & 5 \\  0 & 1 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & -3 & 0 \\  0 & 1 & -\frac{5}{2} \\  0 & 1 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & 0 & -\frac{15}{2} \\  0 & 1 & -\frac{5}{2} \\  0 & 1 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & 0 & -\frac{15}{2} \\  0 & 1 & -\frac{5}{2} \\  0 & 0 & \frac{7}{2} \end{array} \right) \\  \left( \begin{array}{ccc}  1 & 0 & -\frac{15}{2} \\  0 & 1 & -\frac{5}{2} \\  0 & 0 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & 0 & 0 \\  0 & 1 & -\frac{5}{2} \\  0 & 0 & 1 \end{array} \right) \\  \left( \begin{array}{ccc}  1 & 0 & 0 \\  0 & 1 & 0 \\  0 & 0 & 1 \end{array} \right) \end{array}</math>
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==메모==
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* http://math.fullerton.edu/mathews/n2003/GaussianJordanMod.html
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==관련된 항목들==
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* [[가우스 소거법]]
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==매스매티카 파일 및 계산 리소스==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxY2xCTnByU2hWZDg/edit
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q1195020 Q1195020]
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===말뭉치===
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# Here you can solve systems of simultaneous linear equations using Gauss-Jordan Elimination Calculator with complex numbers online for free with a very detailed solution.<ref name="ref_0b4aca7d">[https://matrix.reshish.com/gauss-jordanElimination.php Gauss-Jordan Elimination Calculator]</ref>
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# In fact Gauss-Jordan elimination algorithm is divided into forward elimination and back substitution.<ref name="ref_0b4aca7d" />
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# But practically it is more convenient to eliminate all elements below and above at once when using Gauss-Jordan elimination calculator.<ref name="ref_0b4aca7d" />
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# To understand Gauss-Jordan elimination algorithm better input any example, choose "very detailed solution" option and examine the solution.<ref name="ref_0b4aca7d" />
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# Gauss-Jordan Elimination is an algorithm that can be used to solve systems of linear equations and to find the inverse of any invertible matrix.<ref name="ref_9df6f756">[https://online.stat.psu.edu/statprogram/reviews/matrix-algebra/gauss-jordan-elimination M.7 Gauss-Jordan Elimination]</ref>
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# It's called Gauss-Jordan elimination, to find the inverse of the matrix.<ref name="ref_5de8f0af">[https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-determinants-and-inverses-of-large-matrices/v/inverting-matrices-part-3 Inverting a 3x3 matrix using Gaussian elimination (video)]</ref>
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# And we did this using Gauss-Jordan elimination.<ref name="ref_5de8f0af" />
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# To obtain an initial basic feasible solution, the Gauss-Jordan elimination procedure can be used to convert the Ax = b in the canonical form.<ref name="ref_5dd0e144">[https://www.sciencedirect.com/topics/mathematics/gauss-jordan-elimination Gauss-Jordan Elimination - an overview]</ref>
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# Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination.<ref name="ref_4ea5c7c1">[https://en.wikipedia.org/wiki/Gaussian_elimination Gaussian elimination]</ref>
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# A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists.<ref name="ref_4ea5c7c1" />
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# To convert any matrix to its reduced row echelon form, Gauss-Jordan elimination is performed.<ref name="ref_2442948a">[https://brilliant.org/wiki/gaussian-elimination/ Brilliant Math & Science Wiki]</ref>
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# Gauss-Jordan elimination is a mechanical procedure for transforming a given system of linear equations to \(Rx = d\) with \(R\) in RREF using only elementary row operations.<ref name="ref_ed67f156">[https://people.math.carleton.ca/~kcheung/math/notes/MATH1107/wk04/04_gaussian_elimination.html Gauss-Jordan Elimination]</ref>
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# This more-complete method of solving is called "Gauss-Jordan elimination" (with the equations ending up in what is called "reduced-row-echelon form").<ref name="ref_6a27c3d5">[https://www.purplemath.com/modules/systlin6.htm Systems of Linear Equations: Gaussian Elimination]</ref>
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# Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns.<ref name="ref_079137b8">[https://link.springer.com/article/10.1007/s006070070012 A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices]</ref>
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# Use Gauss-Jordan elimination on augmented matrices to solve a linear system and calculate the matrix inverse.<ref name="ref_0e1a698d">[https://www.mathworks.com/help/matlab/ref/rref.html Reduced row echelon form (Gauss-Jordan elimination)]</ref>
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# We apply the Gauss-Jordan Elimination method: we obtain the reduced row echelon form from the augmented matrix of the equation system by performing elemental operations in rows (or columns).<ref name="ref_fd11c78b">[https://www.matesfacil.com/english/high/solving-systems-by-Gaussian-Elimination.html GAUSSIAN ELIMINATION: SOLVNG LINEAR EQUATION SYSTEMS: EXAMPLES AND SOLVED PROBLEMS: HIGH SCHOOL]</ref>
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# But in case of Gauss-Jordan Elimination Method, we only have to form a reduced row echelon form (diagonal matrix).<ref name="ref_fa645610">[https://www.geeksforgeeks.org/program-for-gauss-jordan-elimination-method/ Program for Gauss-Jordan Elimination Method]</ref>
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# Gauss-Jordan Elimination Method can be used for finding the solution of a systems of linear equations which is applied throughout the mathematics.<ref name="ref_fa645610" />
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# The Gauss-Jordan Elimination method can be used in determining the inverse of a square matrix.<ref name="ref_fa645610" />
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===소스===
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<references />
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[[분류:선형대수학]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q1195020 Q1195020]
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===Spacy 패턴 목록===
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* [{'LOWER': 'gauss'}, {'OP': '*'}, {'LOWER': 'jordan'}, {'LEMMA': 'elimination'}]

2021년 2월 17일 (수) 04:56 기준 최신판

개요

  • 선형대수학의 중요한 알고리즘의 하나
  • 선형연립방정식의 해법, 역행렬의 계산 등에 활용할 수 있다



예

\(\left( \begin{array}{ccc} 1 & -3 & 0 \\ -1 & 1 & 5 \\ 0 & 1 & 1 \end{array} \right)\) 에 가우스-조단 소거법을 적용한 경우


\(\begin{array}{l} \left( \begin{array}{ccc} 1 & -3 & 0 \\ -1 & 1 & 5 \\ 0 & 1 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & -3 & 0 \\ 0 & -2 & 5 \\ 0 & 1 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & -3 & 0 \\ 0 & 1 & -\frac{5}{2} \\ 0 & 1 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & -\frac{15}{2} \\ 0 & 1 & -\frac{5}{2} \\ 0 & 1 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & -\frac{15}{2} \\ 0 & 1 & -\frac{5}{2} \\ 0 & 0 & \frac{7}{2} \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & -\frac{15}{2} \\ 0 & 1 & -\frac{5}{2} \\ 0 & 0 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & -\frac{5}{2} \\ 0 & 0 & 1 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right) \end{array}\)



메모

관련된 항목들

매스매티카 파일 및 계산 리소스

노트

위키데이터

말뭉치

  1. Here you can solve systems of simultaneous linear equations using Gauss-Jordan Elimination Calculator with complex numbers online for free with a very detailed solution.[1]
  2. In fact Gauss-Jordan elimination algorithm is divided into forward elimination and back substitution.[1]
  3. But practically it is more convenient to eliminate all elements below and above at once when using Gauss-Jordan elimination calculator.[1]
  4. To understand Gauss-Jordan elimination algorithm better input any example, choose "very detailed solution" option and examine the solution.[1]
  5. Gauss-Jordan Elimination is an algorithm that can be used to solve systems of linear equations and to find the inverse of any invertible matrix.[2]
  6. It's called Gauss-Jordan elimination, to find the inverse of the matrix.[3]
  7. And we did this using Gauss-Jordan elimination.[3]
  8. To obtain an initial basic feasible solution, the Gauss-Jordan elimination procedure can be used to convert the Ax = b in the canonical form.[4]
  9. Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination.[5]
  10. A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists.[5]
  11. To convert any matrix to its reduced row echelon form, Gauss-Jordan elimination is performed.[6]
  12. Gauss-Jordan elimination is a mechanical procedure for transforming a given system of linear equations to \(Rx = d\) with \(R\) in RREF using only elementary row operations.[7]
  13. This more-complete method of solving is called "Gauss-Jordan elimination" (with the equations ending up in what is called "reduced-row-echelon form").[8]
  14. Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns.[9]
  15. Use Gauss-Jordan elimination on augmented matrices to solve a linear system and calculate the matrix inverse.[10]
  16. We apply the Gauss-Jordan Elimination method: we obtain the reduced row echelon form from the augmented matrix of the equation system by performing elemental operations in rows (or columns).[11]
  17. But in case of Gauss-Jordan Elimination Method, we only have to form a reduced row echelon form (diagonal matrix).[12]
  18. Gauss-Jordan Elimination Method can be used for finding the solution of a systems of linear equations which is applied throughout the mathematics.[12]
  19. The Gauss-Jordan Elimination method can be used in determining the inverse of a square matrix.[12]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Gauss-Jordan Elimination Calculator
  2. ↑ M.7 Gauss-Jordan Elimination
  3. ↑ 3.0 3.1 Inverting a 3x3 matrix using Gaussian elimination (video)
  4. ↑ Gauss-Jordan Elimination - an overview
  5. ↑ 5.0 5.1 Gaussian elimination
  6. ↑ Brilliant Math & Science Wiki
  7. ↑ Gauss-Jordan Elimination
  8. ↑ Systems of Linear Equations: Gaussian Elimination
  9. ↑ A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices
  10. ↑ Reduced row echelon form (Gauss-Jordan elimination)
  11. ↑ GAUSSIAN ELIMINATION: SOLVNG LINEAR EQUATION SYSTEMS: EXAMPLES AND SOLVED PROBLEMS: HIGH SCHOOL
  12. ↑ 12.0 12.1 12.2 Program for Gauss-Jordan Elimination Method

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'gauss'}, {'OP': '*'}, {'LOWER': 'jordan'}, {'LEMMA': 'elimination'}]
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