|
In mathematics, the term linear function refers to two distinct but related notions:〔"The term ''linear function'', which is not used here, means a linear form in some textbooks and an affine function in others." Vaserstein 2006, p. 50-1〕 * In calculus and related areas, a linear function is a polynomial function of degree zero or one, or is the zero polynomial.〔Stewart 2012, p. 23〕 * In linear algebra and functional analysis, a linear function is a linear map.〔Shores 2007, p. 71〕 == As a polynomial function == (詳細はanalytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero). When the function is of only one variable, it is of the form : where and are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. is frequently referred to as the slope of the line, and as the intercept. For a function of any finite number of independent variables, the general formula is :, and the graph is a hyperplane of dimension . A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one independent variable, is a horizontal line. In this context, the other meaning (a linear map) may be referred to as a homogeneous linear function or a linear form. In the context of linear algebra, this meaning (polynomial functions of degree 0 or 1) is a special kind of affine map. 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「Linear function」の詳細全文を読む スポンサード リンク
|