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Linear map or polynomial function of degree one
mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is
Linear_function
Type of mathematical function
piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear function
Piecewise_linear_function
Polynomial function of degree at most one
calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates)
Linear_function_(calculus)
Mathematical function, in linear algebra
mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which respects
Linear_map
Method of curve fitting
{\displaystyle C^{0}} . Linear interpolation is often used to approximate a value of some function f using two known values of that function at other points.
Linear_interpolation
Method to solve optimization problems
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints
Linear_programming
System where changes of output are not proportional to changes of input
known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives
Nonlinear_system
Properties of mathematical relationships
mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial.
Linearity
Class of statistical models
a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were
Generalized_linear_model
Least squares approximation of linear functions to data
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems
Linear_least_squares
Method used in statistics, pattern recognition, and other fields
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization
Linear_discriminant_analysis
Statistical modeling method
than a single dependent variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are
Linear_regression
Linear function of explanatory variables used to predict a dependent variable
In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables
Linear_predictor_function
Type of activation function
(rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU (
Rectified_linear_unit
Finding linear approximation of function at given point
mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation
Linearization
Mathematical activation function in data analysis
shrinkage function defined in . Variants of the swish function include Mish. For β = 0, the function is linear: f(x) = x/2. For β = 1, the function is the
Swish_function
Geometric transformation that preserves lines but not angles nor the origin
to be viewed as vectors and vice versa. For any linear transformation λ of V, we can define the function L(c, λ) : X → X by L ( c , λ ) ( x ) = m c − 1
Affine_transformation
Linear regression model with a single explanatory variable
finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent
Simple_linear_regression
Mathematical function whose derivative exists
function has a non-vertical tangent line at each interior point in its domain. A differentiable function is locally approximable by a linear function
Differentiable_function
Function returning one of only two values
all (linear) combinations of at most m arguments Evasive: if evaluation of the function always requires the value of all arguments A Boolean function is
Boolean_function
Set of functions between two fixed sets
X: the set of linear functionals X → F with addition and scalar multiplication defined pointwise. The cardinal dimension of a function space with no extra
Function_space
Relationship of a signal transducer
A linear response function describes the input-output relationship of a signal transducer, such as a radio turning electromagnetic waves into music or
Linear_response_function
Approximation of a function by its tangent line at a point
mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely
Linear_approximation
Equation that does not involve powers or products of variables
The functions whose graph is a line are generally called linear functions in the context of calculus. However, in linear algebra, a linear function is
Linear_equation
Vector-valued function of multiple vectors, linear in each argument
In linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map
Multilinear_map
Search problem in quantum mechanics
linear function problem, is a search problem that generalizes the Bernstein–Vazirani problem. In the Bernstein–Vazirani problem, the hidden function is
Hidden linear function problem
Hidden_linear_function_problem
Function defined by multiple sub-functions
Terms like piecewise linear, piecewise smooth, piecewise continuous, and others are also very common. The meaning of a function being piecewise P {\displaystyle
Piecewise_function
Branch of mathematics
mathematical analysis, may be viewed as the application of linear algebra to function spaces. Linear algebra is also used in most sciences and fields of engineering
Linear_algebra
Type of statistical model
linear model Generalized linear model Linear predictor function Linear system Linear regression Statistical model Priestley, M.B. (1988) Non-linear and
Linear_model
Solution process for some optimization problems
problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation
Nonlinear_programming
Differential equation that is linear with respect to the unknown function
In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written
Linear_differential_equation
Special type of Boolean function
bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when
Bent_function
Linear combination of indicator functions of real intervals
mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals
Step_function
In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as
Discontinuous_linear_map
Type of shift register in computing
linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function
Linear-feedback shift register
Linear-feedback_shift_register
Mathematical function conceived as a crude model
they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing,
Artificial_neuron
Function between topological vector spaces
related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector
Continuous_linear_operator
Association of one output to each input
include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain
Function_(mathematics)
Fundamental principle of physics
response (X + Y). A function F ( x ) {\displaystyle F(x)} that satisfies the superposition principle is called a linear function. Superposition can be
Superposition_principle
Inequality which involves a linear function
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: <
Linear_inequality
Real function with secant line between points above the graph itself
line like a linear function), while a concave function's graph is shaped like a cap ∩ {\displaystyle \cap } . A twice-differentiable function of a single
Convex_function
Indicator for how well data points fit a line or curve
be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases
Coefficient_of_determination
Numerical measure of a statistical relationship between variables
coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may be two columns
Correlation_coefficient
Fundamental theorem in probability theory and statistics
number of edges, and in fact, faces of all dimensions. A linear function of a matrix M is a linear combination of its elements (with given coefficients)
Central_limit_theorem
Flaw in mathematical modelling
slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent
Overfitting
Statistical relationship
sensitive only to a linear relationship between two variables (which in turn may be present even when one variable is a nonlinear function of the other). Other
Correlation
Concept in mathematical optimization
linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function
Linear-fractional_programming
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Pattern defining an infinite sequence of numbers
calculated by repeatedly applying the equation. In linear recurrences, the nth term is equated to a linear function of the k {\displaystyle k} previous terms.
Recurrence_relation
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Artificial neural network node function
performance, activation functions also have different mathematical properties: Nonlinear When the activation function is non-linear, then a two-layer neural
Activation_function
Kind of linear transformation
bounded linear operator is a special kind of linear transformation that is particularly important in infinite dimensions. In finite dimensions, a linear transformation
Bounded_operator
Extension of evidence theory to continuous variables of interest
Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples
Linear_belief_function
Smooth approximation of one-hot arg max
linear discriminant analysis, the input to the function is the result of K distinct linear functions, and the predicted probability for the jth class
Softmax_function
Filter whose phase response is proportional to frequency
In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency. The result is that
Linear_phase
Type of vector space in math
a continuous and bijective linear function from one Banach space to another is an isomorphism (that is, a continuous linear map whose inverse is also continuous)
Hilbert_space
Estimate of time taken for running an algorithm
the type of function appearing in the big O notation. For example, an algorithm with time complexity O ( n ) {\displaystyle O(n)} is a linear time algorithm
Time_complexity
Method for estimating new data within known data points
interpolation is a generalization of linear interpolation. Note that the linear interpolant is a linear function. We now replace this interpolant with
Interpolation
General form of cryptanalysis applicable primarily to block ciphers
in the LSB) occurs with probability of 4/256 (possible with the non-linear function in the AES cipher for instance) then for only 4 values (or 2 pairs)
Differential_cryptanalysis
Numerical method for solving physical or engineering problems
\Omega } in the plane (below), and a piecewise linear function (above, in color) of this polygon which is linear on each triangle of the triangulation; the
Finite_element_method
Class of pseudorandom number generators
combining them with a non-linear function, as described in the original paper. Because plain xorshift generators (without a non-linear step) fail some statistical
Xorshift
Method for estimating the unknown parameters in a linear regression model
input dataset and the output of the (linear) function of the independent variable. Some sources consider OLS to be linear regression. Geometrically, this is
Ordinary_least_squares
Tent function, often used in signal processing
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often
Triangular_function
Mathematical operation that predicts future values of a discrete-time signal
Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In
Linear_prediction
Function, homomorphism, or morphism
special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this
Map_(mathematics)
Algebraic structure in linear algebra
In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")
Vector_space
Statistical method of dividing data into equal-sized intervals for analysis
floor and ceiling functions). The first three are piecewise constant, changing abruptly at each data point, while the last six use linear interpolation between
Quantile
Algorithms for solving convex optimization problems
where f is a convex function and G is a convex set. Without loss of generality, we can assume that the objective f is a linear function. Usually, the convex
Interior-point_method
Types of mappings in mathematics
certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous
Functional_(mathematics)
Type of Turing machine
In computer science, a linear bounded automaton (abbreviated LBA) is a restricted form of Turing machine that functions as a more accurate model of a real-world
Linear_bounded_automaton
Area of mathematics
structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The
Functional_analysis
Method for the construction of fractals
k-ary tree, also known as a Cayley tree. Sometimes each function fi is required to be a linear, or more generally an affine transformation, and hence represented
Iterated_function_system
About polynomials in several variables
if the degree of the polynomial is 1 , {\displaystyle 1,} and linear polynomial functions are invertible. On July 19, 2026, Levent Alpöge presented an
Jacobian_conjecture
Statistical model for a binary dependent variable
classifier. Analogous linear models for binary variables with a different sigmoid function instead of the logistic function (to convert the linear combination to
Logistic_regression
Statistical modeling technique
regression expresses the conditional quantiles of a dependent variable as a linear function of the explanatory variables. Crucial to the practicality of quantile
Quantile_regression
Notion in calculus
part of the increment of a function. This leads directly to the notion that the differential of a function at a point is a linear functional of an increment
Differential_of_a_function
Generalized function whose value is zero everywhere except at zero
developed the theory of distributions, where it is defined as a linear form acting on functions. The graph of the Dirac delta is usually thought of as following
Dirac_delta_function
Algorithm for supervised learning of binary classifiers
is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier
Perceptron
Process by which a quantum system takes on a definitive state
( s z {\displaystyle s_{z}} ), and so on. The observable acts as a linear function on the states of the system; its eigenvectors correspond to the quantum
Wave_function_collapse
Optimization algorithm
Frank–Wolfe algorithm considers a linear approximation of the objective function, and moves towards a minimizer of this linear function (taken over the same domain)
Frank–Wolfe_algorithm
Time series model
series. An MA model expresses the current value of a time series as a linear function of current and past random shocks (error terms) with finite lag length
Moving-average_model
Type of feedforward neural network
with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks
Multilayer_perceptron
of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial, graph
List of mathematical functions
List_of_mathematical_functions
Type of mathematical expression
Product-to-sum identities, into a linear combination of functions sin(nx) and cos(nx). This equivalence explains why linear combinations are called polynomials
Polynomial
Standard for HDTV image encoding and signal characteristics
color) modified by the non-linear function above. However, since E Y ′ {\displaystyle E'_{Y}} is computed from the non-linear RGB components, this equivalence
Rec._709
Notion in supervised machine learning
high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity
Vapnik–Chervonenkis_dimension
Subset of artificial intelligence
and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons
Machine_learning
output amplitude is not a linear function of the input amplitude under specified conditions. Generally, output is a linear function of input only for a fixed
Amplitude_distortion
Mathematical form
\\u_{1}&u_{2}&u_{3}\\v_{1}&v_{2}&v_{3}\\\end{vmatrix}}} A linear mapping can be defined as a function f between two vector spaces V and W with underlying field
Product_(mathematics)
Method for estimating new data outside known data points
provide good results when used to extend the graph of an approximately linear function or not too far beyond the known data. If the two data points nearest
Extrapolation
Theorem related to ordinary least squares
every other linear unbiased estimator β ~ {\displaystyle {\widetilde {\beta }}} . The ordinary least squares estimator (OLS) is the function β ^ = ( X T
Gauss–Markov_theorem
Type of function in linear algebra
In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm, on a vector space is
Sublinear_function
Linear map from a vector space to its field of scalars
the left). The constant zero function, mapping every vector to zero, is trivially a linear functional. Every other linear functional (such as the ones
Linear_form
Instantaneous rate of change (mathematics)
tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. The derivative
Derivative
Extension of cubic spline interpolation
image (the continuous function before sampling). A clear example of this effect is when the original image is a linear function (a simple gradient image)
Bicubic_interpolation
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
Undeciphered writing system of ancient Crete
contains Linear A Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear A. Linear A is
Linear_A
Element of a basis for a function space
a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination
Basis_function
Mathematical algorithm
algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of
Gauss–Newton_algorithm
Numbers obtained by adding the two previous ones
{\displaystyle \varphi ^{n}} as a linear function of lower powers, which in turn can be decomposed all the way down to a linear combination of φ {\displaystyle
Fibonacci_sequence
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