Linear Function

The subject of linear function encompasses a wide range of important elements. linear algebra - How to check the linearity of a function .... You know that a linear function satisfies the following property: $$f (a+b)=f (a)+f (b)$$ and you want to determine whether a particular function $g$ is linear, so you just check whether this property holds. real analysis - maximum of a linear function on a convex set .... How to prove that any linear function which is defined on a convex subset of $\\mathbb{R}^n$ attains its maximum always at one of the extreme points of the set?

Thank you for the hint! What is the difference between linear and affine function?. A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so while the linear part fixes the origin, the translation can map it somewhere else.

Is the absolute value function a linear function?. I would simply define a linear function as always having the same slope (and, more technically, it must be continuous). Clearly, the absolute value function has a negative slope for values < 0 and positive slope for values > 0. sequences and series - Are linear functions always continuous .... Similarly, such a function may also be called a linear map.

Note that this is different from the middle school definition of a linear function in two very important ways: first, the definition applies to functions with arbitrary vector spaces for domain and codomain, rather than the real numbers; and second, a linear function must be zero at zero. Why are linear functions linear? Similarly, - Mathematics Stack Exchange. That's why I emphasized the distinction between a linear function in the context of calculus, and in the context of linear algebra and functional analysis.

Although I do agree that calling it affine would have been much better. Equally important, sOLUTION: Suppose that the weight (in pounds) of an airplane is a .... Question 358837: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 15 gallons of fuel, the airplane weighs 2187 pounds. real analysis - What's an example of a discontinuous linear functional ....

31 You won't find an explicit example of a discontinuous linear functional defined everywhere on a Banach space: these require the Axiom of Choice. However, you can find a discontinuous linear functional on a normed linear space. Additionally, algebra precalculus - Is constant function also a linear function .... 7 It depends on how you define "a linear function" The graph is a horizontal line. Often times, books describe linear functions as polynomials of degree 1, which would require a nonzero slope, so would call this a constant function instead. Generally, when we discuss something being linear, we mean it scales with the input.

Additionally, real analysis - What is a "linear function" in the context of .... What you write is an affine function.