is generally no: there exist discontinuous linear maps. If the domain of definition is complete, it is trickier; such maps can be proven to exist, but...

infinite-dimensional normed space, there exists some discontinuous linear functional. The Conway base 13 function is discontinuous at every point. A real function f {\displaystyle...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

(respectively, bounded), or else all three are discontinuous (respectively, unbounded). Every linear map whose domain is a finite-dimensional Hausdorff...

Piecewise linear function Linear approximation Linear interpolation Discontinuous linear map Linear least squares "The term linear function means a linear form...

(operator theory) – Bounded operators with sub-unit norm Discontinuous linear map Continuous linear operator – Function between topological vector spaces...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

the Banach–Steinhaus theorem) states that a set H {\displaystyle H} of linear maps between Banach spaces is equicontinuous if it is pointwise bounded; that...

spaces. Informally, the operator norm ‖ T ‖ {\displaystyle \|T\|} of a linear map T : X → Y {\displaystyle T:X\to Y} is the maximum factor by which it "lengthens"...

infinite-dimensional normed space, as shown by the example of discontinuous linear maps. Nevertheless, in the theory of topological vector spaces the...

u(0)=u_{0}{\text{ (1)}}} , where A is a linear operator mapping a dense linear subspace D(A) of X into X (see discontinuous linear map), with u ( t ) = S ( t ) u 0...

every infinite-dimensional topological vector space there is a discontinuous linear map. General topology A uniform space is compact if and only if it...

Differential equations of mathematical physics Dirichlet function Discontinuous linear map Efron's non-transitive dice Example of a game without a value Examples...

then the identity map Id : ( X , τ ) → ( X , ν ) {\displaystyle \operatorname {Id} :(X,\tau )\to (X,\nu )} a closed discontinuous linear operator. Consider...

every operator, which is a purely algebraic fact explained at Discontinuous linear map § General existence theorem and based on the axiom of choice. If...

Closed linear operator – Linear operator whose graph is closed Discontinuous linear map Kakutani fixed-point theorem – Fixed-point theorem for set-valued...

the map g ↦ g⋅x is smooth. There is a well-developed theory of Lie group actions, i.e. action which are smooth on the whole space. If g acts by linear transformations...

with discontinuous marks like diacritics can be characterized as less linear than those without. In the initial historical distinction, linear writing...

assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Until the 19th century...

peculiar to non-linear systems alone and it can also be exhibited by infinite dimensional linear systems. As mentioned above, the logistic map itself is an...

operator – Function that is defined almost everywhere (mathematics) Discontinuous linear map Kakutani fixed-point theorem – Fixed-point theorem for set-valued...

vector spaces, in which the morphisms ("arrows") are the continuous linear maps. A finite-dimensional example of a continuous embedding is given by a...

A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear...

detail. Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur) and the "Joseph effect" (in which persistence of...

Epitopes are generally divided into two classes: linear and conformational/discontinuous. Linear epitopes are formed by a continuous sequence of amino...

large change is also pictured in the graph. This can be remedied with a discontinuous color function which shows a repeating brightness pattern for the magnitude...

of piecewise linear functions over the mesh, which are continuous at each edge midpoint. Since these functions are generally discontinuous along the edges...

Any linear map f : V → W {\displaystyle f:V\to W} between vector spaces over a field F is homogeneous of degree 1, by the definition of linearity: f (...

all }}x,y\in X.} If u : X → Y {\displaystyle u:X\to Y} is a continuous linear map between normed spaces, then the norm of u {\displaystyle u} and the norm...

beams. Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads...