양의 정부호 행렬(positive definite matrix) - 편집 역사

2021년 2월 17일 (수) 12:52에 Pythagoras0님의 편집

2021-02-17T12:52:42Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T13:20:11Z

메타데이터: 새 문단

2020년 12월 28일 (월) 10:42에 Pythagoras0님의 편집

2020-12-28T10:42:40Z

2020년 11월 16일 (월) 15:28에 Pythagoras0님의 편집

2020-11-16T15:28:14Z

2020년 11월 13일 (금) 14:25에 Pythagoras0님의 편집

2020-11-13T14:25:56Z

2013년 6월 4일 (화) 18:51에 Pythagoras0님의 편집

2013-06-04T18:51:09Z

2013년 3월 13일 (수) 10:14에 Pythagoras0님의 편집

2013-03-13T10:14:00Z

Pythagoras0: 찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

2013-01-15T01:40:35Z

찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

Pythagoras0: 찾아 바꾸기 – “
$” 문자열을 “: ” 문자열로$

2013-01-12T17:57:32Z

찾아 바꾸기 – “<br><math>” 문자열을 “:<math>” 문자열로

2012년 12월 25일 (화) 01:17에 Pythagoras0님의 편집

2012-12-25T01:17:54Z

@@ 112번째 줄: / 112번째 줄: @@
 [[분류:선형대수학]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q77601250 Q77601250]

← 이전 판		2020년 12월 28일 (월) 13:20 판
111번째 줄:		111번째 줄:

	[[분류:선형대수학]]		[[분류:선형대수학]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q77601250 Q77601250]

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
-* 실계수 n×n 행렬 M이 모든 0이 아닌 벡터 v 에 대하여, <math>v^{T}M v > 0 </math> 를 만족시킬 때, 양의 정부호 행렬이라 한다
+* 실계수 n×n 행렬 M이 모든 0이 아닌 벡터 v 에 대하여, <math>v^{T}M v > 0 </math> 를 만족시킬 때, 양의 정부호 행렬이라 한다
 * 실베스터 판정법 - leading principal minor 가 모두 양수이면 양의 정부호 행렬이다
 * 다변수함수의 극점을 분류하는 [[헤세 판정법]] 에 응용할 수 있다
-−
-−
-−
 ==2×2 행렬의 경우==
@@ 19번째 줄: / 19번째 줄: @@
 <math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>
-−
-−
 ==3×3 행렬의 경우==
@@ 33번째 줄: / 33번째 줄: @@
 <math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math>
-−
-−
-−
 ==예==
@@ 44번째 줄: / 44번째 줄: @@
 *  leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll}  \left( \begin{array}{c}  2 \end{array} \right) & 2 \\  \left( \begin{array}{cc}  2 & -1 \\  -1 & 2 \end{array} \right) & 3 \\  \left( \begin{array}{ccc}  2 & -1 & 0 \\  -1 & 2 & -1 \\  0 & -1 & 2 \end{array} \right) & 4 \\  \left( \begin{array}{cccc}  2 & -1 & 0 & 0 \\  -1 & 2 & -1 & 0 \\  0 & -1 & 2 & -1 \\  0 & 0 & -1 & 2 \end{array} \right) & 5 \\  \left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math>
-−
-−
 ==메모==
-−
 * Math Overflow http://mathoverflow.net/search?q=
-−
-−
 ==관련된 항목들==
@@ 64번째 줄: / 64번째 줄: @@
 * [[헤세 판정법]]
-−
-−
 ==매스매티카 파일 및 계산 리소스==
@@ 72번째 줄: / 72번째 줄: @@
 * https://docs.google.com/leaf?id=0B8XXo8Tve1cxMzM0MWEwZjUtYzQzNS00NGEzLTkzNTgtZTc2ZTUyZmNjNWI4&sort=name&layout=list&num=50
-−
 ==수학용어번역==
@@ 83번째 줄: / 83번째 줄: @@
-−
-−
-==사전 형태의 자료==
+==사전 형태의 자료==
 * http://ko.wikipedia.org/wiki/
@@ 93번째 줄: / 93번째 줄: @@
 * http://en.wikipedia.org/wiki/Sylvester's_criterion
-−
 ==리뷰논문, 에세이, 강의노트==
-−
-−
-−
 ==관련논문==
@@ 107번째 줄: / 107번째 줄: @@
 *  Gilbert, George T. 1991. “Positive Definite Matrices and Sylvester’s Criterion”. <em>The American Mathematical Monthly</em> 98 (1) (1월 1): 44-46. doi:[http://dx.doi.org/10.2307/2324036 10.2307/2324036].
-−
-−
 [[분류:선형대수학]]

← 이전 판		2020년 11월 16일 (월) 15:28 판
43번째 줄:		43번째 줄:
	* 다음과 같은 5x5 행렬을 생각하자:<math>\left( \begin{array}{ccccc} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 1 \end{array} \right)</math>		* 다음과 같은 5x5 행렬을 생각하자:<math>\left( \begin{array}{ccccc} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 1 \end{array} \right)</math>
	* leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll} \left( \begin{array}{c} 2 \end{array} \right) & 2 \\ \left( \begin{array}{cc} 2 & -1 \\ -1 & 2 \end{array} \right) & 3 \\ \left( \begin{array}{ccc} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{array} \right) & 4 \\ \left( \begin{array}{cccc} 2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end{array} \right) & 5 \\ \left( \begin{array}{ccccc} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math>		* leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll} \left( \begin{array}{c} 2 \end{array} \right) & 2 \\ \left( \begin{array}{cc} 2 & -1 \\ -1 & 2 \end{array} \right) & 3 \\ \left( \begin{array}{ccc} 2 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2 \end{array} \right) & 4 \\ \left( \begin{array}{cccc} 2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end{array} \right) & 5 \\ \left( \begin{array}{ccccc} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math>
−
−
−
−
−
−	~~==역사==~~
−
−
−
−	* http://www.google.com/search?hl=en&tbs=tl:1&q=
−	* [[수학사 연표]]

@@ 13번째 줄: / 13번째 줄: @@
 ==2×2 행렬의 경우==
-*  행렬:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+*  행렬:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>
 *  principal submatrix
-<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>
 *  leading principal submatrix
-<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>
@@ 25번째 줄: / 25번째 줄: @@
 ==3×3 행렬의 경우==
-*  행렬:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+*  행렬:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math>
 *  principal submatrix
 <math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{3,3} \end{array} \right)</math>
 <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,3} \\  a_{3,1} & a_{3,3} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{2,2} & a_{2,3} \\  a_{3,2} & a_{3,3} \end{array} \right)</math>
-<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math>
 *  leading principal submatrix
-<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math>
@@ 41번째 줄: / 41번째 줄: @@
 ==예==
-*  다음과 같은 5x5 행렬을 생각하자:<math>\left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right)</math><br>
+*  다음과 같은 5x5 행렬을 생각하자:<math>\left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right)</math>
-*  leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll}  \left( \begin{array}{c}  2 \end{array} \right) & 2 \\  \left( \begin{array}{cc}  2 & -1 \\  -1 & 2 \end{array} \right) & 3 \\  \left( \begin{array}{ccc}  2 & -1 & 0 \\  -1 & 2 & -1 \\  0 & -1 & 2 \end{array} \right) & 4 \\  \left( \begin{array}{cccc}  2 & -1 & 0 & 0 \\  -1 & 2 & -1 & 0 \\  0 & -1 & 2 & -1 \\  0 & 0 & -1 & 2 \end{array} \right) & 5 \\  \left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math><br>
+*  leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll}  \left( \begin{array}{c}  2 \end{array} \right) & 2 \\  \left( \begin{array}{cc}  2 & -1 \\  -1 & 2 \end{array} \right) & 3 \\  \left( \begin{array}{ccc}  2 & -1 & 0 \\  -1 & 2 & -1 \\  0 & -1 & 2 \end{array} \right) & 4 \\  \left( \begin{array}{cccc}  2 & -1 & 0 & 0 \\  -1 & 2 & -1 & 0 \\  0 & -1 & 2 & -1 \\  0 & 0 & -1 & 2 \end{array} \right) & 5 \\  \left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math>
@@ 87번째 줄: / 87번째 줄: @@
 ==수학용어번역==
-* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
+* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=definite
 ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=minor

@@ 14번째 줄: / 14번째 줄: @@
 *  행렬:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
-*  principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+*  principal submatrix
-*  leading principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
@@ 24번째 줄: / 26번째 줄: @@
 *  행렬:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
-*  principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{3,3} \end{array} \right)</math>:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,3} \\  a_{3,1} & a_{3,3} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{2,2} & a_{2,3} \\  a_{3,2} & a_{3,3} \end{array} \right)</math>:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+*  principal submatrix
-*  leading principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{3,3} \end{array} \right)</math>
@@ 95번째 줄: / 101번째 줄: @@
 * http://ko.wikipedia.org/wiki/
-* [http://en.wikipedia.org/wiki/Positive-definite_matrix ]http://en.wikipedia.org/wiki/Positive-definite_matrix
+* http://en.wikipedia.org/wiki/Positive-definite_matrix
-* [http://en.wikipedia.org/wiki/Sylvester%27s_criterion http://en.wikipedia.org/wiki/Sylvester's_criterion]
+* http://en.wikipedia.org/wiki/Sylvester's_criterion

← 이전 판		2013년 1월 15일 (화) 01:40 판
55번째 줄:		55번째 줄:

	* http://www.google.com/search?hl=en&tbs=tl:1&q=		* http://www.google.com/search?hl=en&tbs=tl:1&q=
−	* [[~~수학사연표 (역사)\|수학사연표~~]]	+	* [[수학사 연표]]

@@ 21번째 줄: / 21번째 줄: @@
 ==2×2 행렬의 경우==
-*  행렬<br><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+*  행렬:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
-*  principal submatrix<br><math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+*  principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
-*  leading principal submatrix<br><math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
+*  leading principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math><br>
@@ 31번째 줄: / 31번째 줄: @@
 ==3×3 행렬의 경우==
-*  행렬<br><math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+*  행렬:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
-*  principal submatrix<br><math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{3,3} \end{array} \right)</math><br><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,3} \\  a_{3,1} & a_{3,3} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{2,2} & a_{2,3} \\  a_{3,2} & a_{3,3} \end{array} \right)</math><br><math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+*  principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{2,2} \end{array} \right)</math>,<math>\left( \begin{array}{c}  a_{3,3} \end{array} \right)</math>:<math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{1,1} & a_{1,3} \\  a_{3,1} & a_{3,3} \end{array} \right)</math>, <math>\left( \begin{array}{cc}  a_{2,2} & a_{2,3} \\  a_{3,2} & a_{3,3} \end{array} \right)</math>:<math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
-*  leading principal submatrix<br><math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
+*  leading principal submatrix:<math>\left( \begin{array}{c}  a_{1,1} \end{array} \right)</math><math>\left( \begin{array}{cc}  a_{1,1} & a_{1,2} \\  a_{2,1} & a_{2,2} \end{array} \right)</math>, <math>\left( \begin{array}{ccc}  a_{1,1} & a_{1,2} & a_{1,3} \\  a_{2,1} & a_{2,2} & a_{2,3} \\  a_{3,1} & a_{3,2} & a_{3,3} \end{array} \right)</math><br>
@@ 43번째 줄: / 43번째 줄: @@
 ==예==
-*  다음과 같은 5x5 행렬을 생각하자<br><math>\left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right)</math><br>
+*  다음과 같은 5x5 행렬을 생각하자:<math>\left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right)</math><br>
-*  leading principal submatrix와 그 행렬식을 구하면 다음과 같다<br><math>\begin{array}{ll}  \left( \begin{array}{c}  2 \end{array} \right) & 2 \\  \left( \begin{array}{cc}  2 & -1 \\  -1 & 2 \end{array} \right) & 3 \\  \left( \begin{array}{ccc}  2 & -1 & 0 \\  -1 & 2 & -1 \\  0 & -1 & 2 \end{array} \right) & 4 \\  \left( \begin{array}{cccc}  2 & -1 & 0 & 0 \\  -1 & 2 & -1 & 0 \\  0 & -1 & 2 & -1 \\  0 & 0 & -1 & 2 \end{array} \right) & 5 \\  \left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math><br>
+*  leading principal submatrix와 그 행렬식을 구하면 다음과 같다:<math>\begin{array}{ll}  \left( \begin{array}{c}  2 \end{array} \right) & 2 \\  \left( \begin{array}{cc}  2 & -1 \\  -1 & 2 \end{array} \right) & 3 \\  \left( \begin{array}{ccc}  2 & -1 & 0 \\  -1 & 2 & -1 \\  0 & -1 & 2 \end{array} \right) & 4 \\  \left( \begin{array}{cccc}  2 & -1 & 0 & 0 \\  -1 & 2 & -1 & 0 \\  0 & -1 & 2 & -1 \\  0 & 0 & -1 & 2 \end{array} \right) & 5 \\  \left( \begin{array}{ccccc}  2 & -1 & 0 & 0 & 0 \\  -1 & 2 & -1 & 0 & 0 \\  0 & -1 & 2 & -1 & 0 \\  0 & 0 & -1 & 2 & -1 \\  0 & 0 & 0 & -1 & 1 \end{array} \right) & 1 \end{array}</math><br>

← 이전 판	2012년 12월 25일 (화) 01:17 판
143번째 줄:	143번째 줄:


	+	[[분류:선형대수학]]