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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク coefficient ： ウィキペディア英語版 coefficient In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression. For instance in :$7x^2-3xy+1.5+y$ the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as ''a'', ''b'', and ''c'', where "c" is a constant, in :$ax^2+bx+c$ when it is understood that these are not considered variables. Thus a polynomial in one variable ''x'' can be written as :$a\_k\; x^k\; +\; \backslash dotsb\; +\; a\_1\; x^1\; +\; a\_0$ for some integer $k$, where $a\_k,\; \backslash dotsc,\; a\_1,\; a\_0$ are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient. For the largest $i$ with $a\_i\; \backslash ne\; 0$ (if any), $a\_i$ is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial :$\backslash ,\; 4x^5\; +\; x^3\; +\; 2x^2$ is 4. Specific coefficients arise in mathematical identities, such as the binomial theorem which involves binomial coefficients; these particular coefficients are tabulated in Pascal's triangle. ==Linear algebra== In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given :$$ M = \begin 1 & 2 & 0 & 6\\ 0 & 2 & 9 & 4\\ 0 & 0 & 0 & 4\\ 0 & 0 & 0 & 0 \end . The leading coefficient of the first row is 1; 2 is the leading coefficient of the second row; 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient. Though coefficients are frequently viewed as constants in elementary algebra, they can be variables more generally. For example, the coordinates $(x\_1,\; x\_2,\; \backslash dotsc,\; x\_n)$ of a vector $v$ in a vector space with basis $\backslash lbrace\; e\_1,\; e\_2,\; \backslash dotsc,\; e\_n\; \backslash rbrace$, are the coefficients of the basis vectors in the expression :$v\; =\; x\_1\; e\_1\; +\; x\_2\; e\_2\; +\; \backslash dotsb\; +\; x\_n\; e\_n\; .$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「coefficient」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.