Linear (disambiguation)
Linearity is a property of various things in mathematics, physics, and electronics. Linear, linearly, or linearity may also refer to: == Mathematics == Linear approximation table (LAT; also known as correlation matrix), the set of Walsh transforms of linear functions of output bits of a vectorial Boolean function Linear assignment problem, a combinatorial optimization problem about assigning agents to tasks while minimizing total cost, when that is the sum of the costs for each agent Linear bounded automaton (LBA), a Turing machine with the tape size limited to just its input plus endmarkers Linear combination (AKA superposition), an expression constructed from a set of terms by multiplying each term by a constant and adding the results Linear congruential generator (LCG), algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation Linear convergence (to converge linearly), the description of a sequence approaching a limit with convergence order q = 1 and rate μ ∈ (0, 1) Linear function, a function that has some kind of linearity Linear–log (AKA lin–log) plot, a graph with a linear scale on the Y-axis and a log scale on the X-axis Linear logic, a substructural logic that joins the dualities of classical logic with many of the constructive properties of intuitionistic logic Linear programming (LP; also known as linear optimization), a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships Linear recurrence sequence (AKA constant-recursive, linear-recursive, linear-recurrent, C-finite sequence), an infinite list of values that each satisfy a linear equation of a constant number of previous terms Linear recurrence with constant coefficients (AKA linear recurrence relation, linear difference equation), an equation that sets equal to 0 a polynomial that is linear in the various iterates of a variable Linear SAT (LSAT), a Boolean/propositional satisfiability problem with a 3-SAT formula where each clause's set of literals intersects at most one other's, with exactly one literal in common Linear sequence (AKA arithmetic progression, arithmetic sequence), a list of numbers where the difference between consecutive terms remains constant throughout Linear spline, a function defined piecewise by polynomials of degree (at most) 1 Linear term, a component of a formula that contains at most one occurrence of each variable === Abstract algebra and order theory === (Linear) continuum, a generalization of the real number line Linear disjointness (being linearly disjoint), a property of algebras over a field inside a field extension Linear extension, a total order that is compatible with some given partial order Linearly ordered group (AKA totally ordered group), a group with a total order that is translation-invariant Linear order (AKA total order), a binary relation that is not just a partial order but ensures that any two elements are comparable Linear topology, something required for a module to be linearly topologized === Calculus === Linear differential equation, an equality relation between a constant term and the sum of derivatives of a function multiplied by constant coefficients Linear differential operator, a kind of operator defined as a function of the differentiation operator Linearity of differentiation, a property of derivatives in calculus Linearity of integration, a property of integrals in calculus Linear partial differential equation, an equation which involves a multivariable function and one or more of its partial derivatives, when it is linear in the unknown and its derivatives, or (equivalently? ), if it is homogeneous, the sum of any two solutions is also a solution, and any constant multiple of any solution is also a solution === Cryptography and information theory === Linear code, an error-correcting code for which any linear combination of codewords is also a codeword Linear cryptanalysis, a method of breaking a cipher based on finding affine approximations Linear diffusion, the property of a cipher that ensures that a single bit of plaintext results in half of the bits in the ciphertext changing and vice-versa, using a transformation such as multiplication by a matrix over a finite field Linear keyspace (AKA flat key space), the property of a cipher with no weak keys === Geometry === Linear dimension, a 1D subspace in physical space Linear eccentricity (usually denoted c, e, or f), the distance between the center and either focus of an ellipse or hyperbola Linear equivalence, a concept related to divisors in algebraic geometry Linear fractional transformation, an (invertible) homography based on a ratio of linear polynomials Linearly normal (AKA 1-normal), a property in algebraic geometry related to homogeneous coordinate rings Linearly unique polytope (AKA linearly stable polytope), a centrally symmetric partially ordered set with a unique origin symmetric realization up to linear transformations Linear pair of angles, two adjacent angles where their non-shared sides form a straight line, and as such are supplementary Linear separability, the property of two sets of points, where they are linearly separable if there exists at least one line or hyperplane that divides the space such that one set is contained within one side, and the other set within the other side === Linear algebra (including functional analysis) === Linear algebra, the branch of mathematics that studies linear equations, linear maps, vector spaces, and matrices → Outline of linear algebra Linear equation, an equality relation that only involves variables multiplied by numeric coefficients, added up along with a constant term Linear map (AKA linear mapping, linear operator, linear transformation), a function between vector spaces, which preserves the operations of vector addition and scalar multiplication, through the properties of additivity and homogeneity, respectively General linear group, a set of invertible same-size square matrices with the operation of matrix multiplication Honors Advanced Calculus and Linear Algebra, the previous official title of the course Math 55 at Harvard University Linear algebraic group, a subgroup of the group of invertible same-size square matrices under matrix multiplication that is defined by polynomial equations Linear Diophantine equation, a linear equation limited to integer coefficients and solutions Linear form (AKA linear functional, one-form, covector), a linear map from a vector space to its field of scalars Linear group, a set with an operation that is isomorphic to the matrix group, of invertible matrices over a specified field with the operation of matrix multiplication Linear hull, AKA linear span Linear independence (being linearly independent), the property of a set of vectors where none is a linear combination of the others Linear isometry, a linear map between normed vector spaces that preserves the norms Linear space (AKA vector space), a set whose elements (vectors), can be added together and multiplied by numbers (scalars) Linear span (AKA linear hull, span), the smallest linear subspace of a vector space that includes a set of elements Linear subspace (AKA vector subspace), a vector space that is a subset of some larger vector space Linear topological space (AKA topological vector space, TVS, t.v.s.), a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions Linear variety or linear manifold (AKA flat, affine subspace), a subset of an affine space that is itself an affine space Numerical linear algebra (AKA applied linear algebra), the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics Projective linear group (AKA projective general linear group, PGL), the induced action of the general linear group of a vector space on the associated projective space Special linear group, the set of same-size square matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion System of linear equations (AKA linear system), a collection of equalities relating a set of variables === Statistics and machine learning === Bayesian linear regression, a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining posterior probabilities and an out-of-sample prediction of the regressand Best linear unbiased prediction/predictor (BLUP), used in linear mixed models for the estimation of random effects Constrained linear inversion (AKA linear regularization, ridge regression, Tikhonov regularization), a method of estimating the coefficients of multiple-regression models in scenarios where the variables are highly correlated General linear model (AKA general multivariate regression model), a compact way of simultaneously writing several multiple linear regression models using matrices Generalized linear model (GLM), a flexible generalization of ordinary linear regression that allows the linear model to be related to the response variable via a link function and allows the magnitude of the variance of each measurement to be a function of its predicted value Hierarchical linear model (AKA multilevel model), a statistical model of parameters that vary at more than one level, that is a generalization of linear models Linear classifier, a decision algorithm with linear boundaries, i.e.