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  2. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    The y-intercept point (,) = (,) corresponds to buying only 4 kg of sausage; while the x-intercept point (,) = (,) corresponds to buying only 2 kg of salami. Note that the graph includes points with negative values of x or y , which have no meaning in terms of the original variables (unless we imagine selling meat to the butcher).

  3. Linear function - Wikipedia

    en.wikipedia.org/wiki/Linear_function

    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 variable, is a horizontal line. In this context, a function that is also a linear map (the other meaning) may be referred to as a homogeneous linear function or a linear form.

  4. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...

  5. Linearity - Wikipedia

    en.wikipedia.org/wiki/Linearity

    In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.

  6. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The solution set for the equations xy = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

  7. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:

  8. Closed range theorem - Wikipedia

    en.wikipedia.org/wiki/Closed_range_theorem

    Let and be Banach spaces, : a closed linear operator whose domain () is dense in , and ′ the transpose of . The theorem asserts that the following conditions are equivalent: The theorem asserts that the following conditions are equivalent:

  9. Linear differential equation - Wikipedia

    en.wikipedia.org/wiki/Linear_differential_equation

    In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form + ′ + ″ + () = where a 0 (x), ..., a n (x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y (n) are the successive derivatives of an unknown function y of ...