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A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are L p spaces, which are Banach spaces, and especially the L 2 space of square-integrable functions, which is the only Hilbert space among them. Functional ...
In mathematics, the term linear function refers to two distinct but related notions: [1] In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. [2] For distinguishing such a linear function from the other concept, the term affine function is often used ...
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope , which is a set defined as the intersection of finitely many half spaces , each of which is defined by a linear inequality.
Quizlet is a multi-national American company that provides tools for studying and learning. [1] Quizlet was founded in October 2005 by Andrew Sutherland, who at the time was a 15-year old student, [ 2 ] and released to the public in January 2007. [ 3 ]
The tableau is a representation of the linear program where the basic variables are expressed in terms of the non-basic ones: [1]: 65 = + = + where is the vector of m basic variables, is the vector of n non-basic variables, and is the maximization objective.
When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical independence is the same as linear independence. The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent. For example ...
This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem. Similar adjustments can be done in order to allow more tasks than agents, tasks to which multiple agents must be assigned (for instance, a group of more customers than will fit in one taxi), or ...