"기저와 선형결합"의 두 판 사이의 차이
| 8번째 줄: | 8번째 줄: | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <h5>예</h5> | ||
| + | |||
| + | <math>v(1)=\{1, 0\}</math> | ||
| + | |||
| + | <math>v(2)=\{-(\sqrt{3}/2), 1/2\}</math> | ||
<math>\begin{array}{|rcl|} \hline \{1,0\} & = & v(1) \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v(1)+v(2) \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v(1)+\sqrt{3} v(2) \\ \hline \{0,1\} & = & \sqrt{3} v(1)+2 v(2) \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v(1)+\sqrt{3} v(2) \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v(2) \\ \hline \{-1,0\} & = & -v(1) \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v(1)-v(2) \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v(1)-\sqrt{3} v(2) \\ \hline \{0,-1\} & = & -\sqrt{3} v(1)-2 v(2) \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v(1)-\sqrt{3} v(2) \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v(2) \\ \hline \end{array}</math> | <math>\begin{array}{|rcl|} \hline \{1,0\} & = & v(1) \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v(1)+v(2) \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v(1)+\sqrt{3} v(2) \\ \hline \{0,1\} & = & \sqrt{3} v(1)+2 v(2) \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v(1)+\sqrt{3} v(2) \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v(2) \\ \hline \{-1,0\} & = & -v(1) \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v(1)-v(2) \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v(1)-\sqrt{3} v(2) \\ \hline \{0,-1\} & = & -\sqrt{3} v(1)-2 v(2) \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v(1)-\sqrt{3} v(2) \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v(2) \\ \hline \end{array}</math> | ||
| + | |||
| + | <math>\begin{array}{|rcl|} \hline \{1,0\} & = & v_1 \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v_1+v_2 \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v_1+\sqrt{3} v_2 \\ \hline \{0,1\} & = & \sqrt{3} v_1+2 v_2 \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v_1+\sqrt{3} v_2 \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v_2 \\ \hline \{-1,0\} & = & -v_1 \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v_1-v_2 \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v_1-\sqrt{3} v_2 \\ \hline \{0,-1\} & = & -\sqrt{3} v_1-2 v_2 \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v_1-\sqrt{3} v_2 \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v_2 \\ \hline \end{array}</math> | ||
| 53번째 줄: | 65번째 줄: | ||
| + | |||
| + | |||
| + | |||
| + | <h5>매스매티카 파일 및 계산 리소스</h5> | ||
| + | |||
| + | * https://docs.google.com/file/d/0B8XXo8Tve1cxZi1vYlpSZTVoRjQ/edit | ||
| + | * http://www.wolframalpha.com/input/?i= | ||
| + | * http://functions.wolfram.com/ | ||
| + | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | ||
| + | * [http://people.math.sfu.ca/%7Ecbm/aands/toc.htm Abramowitz and Stegun Handbook of mathematical functions] | ||
| + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | ||
| + | * [http://numbers.computation.free.fr/Constants/constants.html Numbers, constants and computation] | ||
| + | * [https://docs.google.com/open?id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록] | ||
2012년 6월 13일 (수) 04:24 판
이 항목의 수학노트 원문주소
개요
예
\(v(1)=\{1, 0\}\)
\(v(2)=\{-(\sqrt{3}/2), 1/2\}\)
\(\begin{array}{|rcl|} \hline \{1,0\} & = & v(1) \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v(1)+v(2) \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v(1)+\sqrt{3} v(2) \\ \hline \{0,1\} & = & \sqrt{3} v(1)+2 v(2) \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v(1)+\sqrt{3} v(2) \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v(2) \\ \hline \{-1,0\} & = & -v(1) \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v(1)-v(2) \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v(1)-\sqrt{3} v(2) \\ \hline \{0,-1\} & = & -\sqrt{3} v(1)-2 v(2) \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v(1)-\sqrt{3} v(2) \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v(2) \\ \hline \end{array}\)
\(\begin{array}{|rcl|} \hline \{1,0\} & = & v_1 \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v_1+v_2 \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v_1+\sqrt{3} v_2 \\ \hline \{0,1\} & = & \sqrt{3} v_1+2 v_2 \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v_1+\sqrt{3} v_2 \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v_2 \\ \hline \{-1,0\} & = & -v_1 \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v_1-v_2 \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v_1-\sqrt{3} v_2 \\ \hline \{0,-1\} & = & -\sqrt{3} v_1-2 v_2 \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v_1-\sqrt{3} v_2 \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v_2 \\ \hline \end{array}\)
역사
메모
- Math Overflow http://mathoverflow.net/search?q=
관련된 항목들
수학용어번역
- 단어사전
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 한국통계학회 통계학 용어 온라인 대조표
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
매스매티카 파일 및 계산 리소스
- https://docs.google.com/file/d/0B8XXo8Tve1cxZi1vYlpSZTVoRjQ/edit
- http://www.wolframalpha.com/input/?i=
- http://functions.wolfram.com/
- NIST Digital Library of Mathematical Functions
- Abramowitz and Stegun Handbook of mathematical functions
- The On-Line Encyclopedia of Integer Sequences
- Numbers, constants and computation
- 매스매티카 파일 목록
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The World of Mathematical Equations
리뷰논문, 에세이, 강의노트
관련논문