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Sum of terms, each multiplied with a scalar
In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding
Linear_combination
Topics referred to by the same term
Symmetry-adapted linear combination may refer to: The linear combination of atomic orbitals in the subject of molecular orbitals Configuration state function
Symmetry-adapted linear combination
Symmetry-adapted_linear_combination
Set of vectors used to define coordinates
written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates
Basis_(linear_algebra)
Linear combination of points where all coefficients are non-negative and sum to 1
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points
Convex_combination
Dimension of the column space of a matrix
2: the first two columns are linearly independent, so the rank is at least 2, but since the third is a linear combination of the first two (the first column
Rank_(linear_algebra)
Linear combination whose coefficients sum to 1
In mathematics, an affine combination of x1, ..., xn is a linear combination ∑ i = 1 n α i ⋅ x i = α 1 x 1 + α 2 x 2 + ⋯ + α n x n , {\displaystyle \sum
Affine_combination
In linear algebra, generated subspace
K} , and multiplying a linear combination of S by a scalar c ∈ K {\displaystyle c\in K} will produce another linear combination of S: c ( λ 1 v 1 + ⋯ +
Linear_span
Method used in statistics, pattern recognition, and other fields
generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes
Linear_discriminant_analysis
Vectors whose linear combinations are nonzero
In linear algebra, a set of vectors is said to be linearly independent if there exists no vector in the set that is equal to a linear combination of the
Linear_independence
Algebraic structure in linear algebra
are linearly independent if a linear combination results in the zero vector if and only if all its coefficients are zero. Linear subspace A linear subspace
Vector_space
Statistical model for a binary dependent variable
is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis, logistic
Logistic_regression
Theorem related to ordinary least squares
\varepsilon _{j})=0,\forall i\neq j.} A linear estimator of β j {\displaystyle \beta _{j}} is a linear combination β ^ j = c 1 j y 1 + ⋯ + c n j y n , {\displaystyle
Gauss–Markov_theorem
System where changes of output are not proportional to changes of input
linear combination of the unknown variables or functions that appear in them. Systems can be defined as nonlinear, regardless of whether known linear
Nonlinear_system
Principle of quantum mechanics
equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions
Quantum_superposition
Relating two numbers and their greatest common divisor
b=69} is d = 3 {\displaystyle d=3} , which can be written as the linear combination a x + b y = 15 ( − 9 ) + 69 ( 2 ) = 3 {\displaystyle ax+by=15(-9)+69(2)=3}
Bézout's_identity
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Statistical measure of how far values spread from their average
general Bienaymé's identity. These results lead to the variance of a linear combination as: Var ( ∑ i = 1 N a i X i ) = ∑ i , j = 1 N a i a j Cov ( X
Variance
Type of mathematical system
{\displaystyle \mathbf {y} (t)} are two valid solutions, then so is any linear combination of the two solutions, e.g., z ( t ) = d e f α x ( t ) + β y (
Linear_dynamical_system
Several equations of degree 1 to be solved simultaneously
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example
System_of_linear_equations
Projection of data onto lower-dimensional manifolds
high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear decomposition methods, onto lower-dimensional
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Class of statistical models
Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a
Generalized_linear_model
Differential equation that is linear with respect to the unknown function
identity mapping. A linear differential operator (abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential
Linear_differential_equation
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
Linear combination of indicator functions of real intervals
numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function
Step_function
Statistical classification in machine learning
In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. A simpler definition
Linear_classifier
In mathematics, vector subspace
specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is
Linear_subspace
Method for describing the electronic structure of molecules using quantum mechanics
by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used in computational chemistry. An additional
Molecular_orbital_theory
Physical system satisfying the superposition principle
The superposition principle means that a linear combination of inputs to the system produces a linear combination of the individual zero-state outputs (that
Linear_system
Mathematical function conceived as a crude model
but they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing
Artificial_neuron
Number of subsets of a given size
polynomial p(t) of degree at most d is uniquely expressible as a linear combination ∑ k = 0 d a k ( t k ) {\textstyle \sum _{k=0}^{d}a_{k}{\binom {t}{k}}}
Binomial_coefficient
Approximation method in statistics
its partial derivatives. A regression model is a linear one when the model comprises a linear combination of the parameters, i.e., f ( x , β ) = ∑ j = 1
Least_squares
Approximation method in quantum physics
completely non-relativistic. The variational solution is assumed to be a linear combination of a finite number of basis functions, which are usually (but not
Hartree–Fock_method
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Mathematical function defined piecewise by polynomials
coefficients of the linear combination of those basis polynomials that give the spline on that interval c0, ..., ck–2 Add up that linear combination of basis polynomial
Spline_(mathematics)
Probability distribution and special case of gamma distribution
S2CID 19777585. Bausch, J. (2013). "On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String
Chi-squared_distribution
Technique in quantum chemistry
A linear combination of atomic orbitals (LCAO) is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum
Linear combination of atomic orbitals
Linear_combination_of_atomic_orbitals
Set of statistical processes for estimating the relationships among variables
common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data
Regression_analysis
Class of iterative numerical methods for solving differential equations
previous points and derivative values. In the case of linear multistep methods, a linear combination of the previous points and derivative values is used
Linear_multistep_method
hull of S {\displaystyle S} is a closed set. Affine combination Convex combination Linear combination Convex Analysis and Minimization Algorithms by Jean-Baptiste
Conical_combination
Set of functions used to represent the electronic wave function
{\displaystyle |\psi _{i}\rangle } are expanded within the basis set as a linear combination of the basis functions | ψ i ⟩ ≈ ∑ μ c μ i | μ ⟩ {\textstyle |\psi
Basis_set_(chemistry)
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
Mathematical entity to describe the probability of each possible measurement on a system
uncertainty for the given observable. Using bra–ket notation, this linear combination of eigenstates can be represented as: | Ψ ( t ) ⟩ = ∑ n C n ( t )
Quantum_state
Method for solving continuous operator problems (such as differential equations)
representing the system energy and the approximate solution is a linear combination of the given set of the basis functions. Bubnov–Galerkin method (after
Galerkin_method
Wave shaped like the sine function
zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the sine
Sine_wave
Linear map from a vector space to its field of scalars
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
Linear_form
Method for estimating the unknown parameters in a linear regression model
{\beta }}} is linear in y, meaning that it represents a linear combination of the dependent variables yi. The weights in this linear combination are functions
Ordinary_least_squares
Indicator for how well data points fit a line or curve
the proportion of variability in Yi that may be attributed to some linear combination of the regressors (explanatory variables) in X. R2 is often interpreted
Coefficient_of_determination
Method of modeling the behavior of a viscoelastic material
method of modeling the behavior of a viscoelastic material using a linear combination of springs and dashpots to represent elastic and viscous components
Standard_linear_solid_model
Machine learning technique
The slow network learns by gradient descent. It was later renamed as "linearized self-attention". Bahdanau-style attention, also referred to as additive
Attention_(machine_learning)
Mathematical model
A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model
Log-linear_model
Formal linear combination in a cell complex
In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes)
Chain_(algebraic_topology)
Complex number representing a particular sine wave
the complex amplitude (phasor). A linear combination of such functions can be represented as a linear combination of phasors (known as phasor arithmetic
Phasor
Description of a quantum-mechanical system
observable in that eigenstate. More generally, a quantum state will be a linear combination of the eigenstates, known as a quantum superposition. When an observable
Schrödinger_equation
Special mathematical functions defined on the surface of a sphere
period evenly divides 2π, m is necessarily an integer and Φ is a linear combination of the complex exponentials e± imφ. The solution function Y(θ, φ)
Spherical_harmonics
Probability distribution
properties that are valuable in analytic studies. For instance, any linear combination of a fixed collection of independent normal deviates is a normal deviate
Normal_distribution
Method of statistical analysis
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables
Bayesian_linear_regression
Function used in computer graphics
Davis, is based on the fact that any point on the curve must be a linear combination of the ends. Let p0 and p1 be the first and last points of the arc
Spherical linear interpolation
Spherical_linear_interpolation
In linear algebra, relation between 3 dimensions
The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity
Rank–nullity_theorem
Unsolved problem in geometry
non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties
Hodge_conjecture
combinations. affine combination A linear combination in which the sum of the coefficients is 1. basis In a vector space, a linearly independent set of
Glossary_of_linear_algebra
Statistical property of collections of time series data
In such cases, the variables may drift in the short run, but their linear combination is stationary, implying that they move together over time and remain
Cointegration
Computer hardware technology that uses quantum mechanics
which can be in one of two states (a binary), a qubit can exist in a linear combination of two states known as a quantum superposition. The result of measuring
Quantum_computing
Statistical model used in time series analysis
series depends linearly on its own past values (lags), while the MA component specifies that the current value depends on a linear combination of past error
Autoregressive moving-average model
Autoregressive_moving-average_model
Chemical bond by sharing of electron pairs
performing a linear combination of contributing structures (resonance) if there are several of them. In contrast, for molecular orbital theory, a linear combination
Covalent_bond
Vector of length one
a vector space, and every vector in the space may be written as a linear combination form of unit vectors. Unit vectors may be used to represent the axes
Unit_vector
Method to solve constrained optimization problems
the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the Lagrange
Lagrange_multiplier
Matrices important in quantum mechanics and the study of spin
{\displaystyle 2\times 2} Hermitian matrix can be written in a unique way as a linear combination of Pauli matrices, with all coefficients being real numbers. The Pauli
Pauli_matrices
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Generalization of the one-dimensional normal distribution to higher dimensions
random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance
Multivariate normal distribution
Multivariate_normal_distribution
Topics referred to by the same term
each agent Linear bounded automaton (LBA), a Turing machine with the tape size limited to just its input plus endmarkers Linear combination (AKA superposition)
Linear_(disambiguation)
Electronic circuits obeying the superposition principle
the circuit F(x) when a linear combination of signals ax1(t) + bx2(t) is applied to it is equal to the linear combination of the outputs due to the signals
Linear_circuit
Algorithm for computing greatest common divisors
using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each
Euclidean_algorithm
Association of atoms to form chemical compounds
hybridization and resonance, and molecular orbital theory, which includes the linear combination of atomic orbitals and ligand field theory. Electrostatics is used
Chemical_bond
Effect of variables' uncertainties on the uncertainty of a function based on them
which are linear combinations of n {\displaystyle n} variables x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} with combination coefficients
Propagation_of_uncertainty
Array of numbers
product of outgoing particle states and a linear combination of ingoing particle states. The linear combination is given by a matrix known as the S-matrix
Matrix_(mathematics)
Structure in biology and artificial intelligence
layer). The "signal" input to each neuron is a number, specifically a linear combination of the outputs of the connected neurons in the previous layer. The
Neural_network
Second-order partial differential equation
solutions to Laplace's equation (or any linear homogeneous differential equation), their sum (or any linear combination) is also a solution. This property
Laplace's_equation
Class of error-correcting code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally
Linear_code
Index of articles associated with the same name
In mathematics, a formal sum, formal series, or formal linear combination may be: In group theory, an element of a free abelian group, a sum of finitely
Formal_sum
Vector spaces associated to a matrix
Given a matrix A, the action of the matrix A on a vector x returns a linear combination of the columns of A with the coordinates of x as coefficients; that
Row_and_column_spaces
Vector field in Riemannian geometry
{\displaystyle T=a{\dot {\gamma }}(t)+bt{\dot {\gamma }}(t)} is a linear combination of trivial Jacobi fields and I ( t ) {\displaystyle I(t)} is orthogonal
Jacobi_field
Type of artificial neural network
functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial
Radial_basis_function_network
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
one is a linear combination of the other two. Picking any two defines m {\displaystyle {\mathfrak {m}}} ; the remaining degenerate linear combinations
Killing_vector_field
Concept in statistics
statistics, particularly in the analysis of variance and linear regression, a contrast is a linear combination of variables (parameters or statistics) whose coefficients
Contrast_(statistics)
In mathematics, invariant of square matrices
computed by the Laplace expansion, which expresses the determinant as a linear combination of determinants of submatrices, or with Gaussian elimination, which
Determinant
Vectors mapped to 0 by a linear map
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of
Kernel_(linear_algebra)
Type of boundary condition in mathematics
differential equations. The Robin boundary condition specifies a linear combination of the value of a function and the value of its derivative at the
Robin_boundary_condition
to a set of linear equations by directly minimizing an error residual (e.g. a Newton–Raphson step size) with respect to a linear combination of known sample
DIIS
{f''(x)}}}\right|\leq 1} and satisfies f ‴ ( x ) = 0 {\displaystyle f'''(x)=0} elsewhere. Linear and convex quadratic functions are self-concordant, since their third derivative
Self-concordant_function
Spline function
spline function of a specific degree can be uniquely expressed as a linear combination of B-splines of that degree over the same knots, a property that makes
B-spline
Algebraic object with geometric applications
space V with the space V∗ by first decomposing the tensor into a linear combination of simple tensors, and then applying a factor from V∗ to a factor
Tensor
Function in discrete mathematics
eigenvectors is known. Moreover, the eigenvectors are not unique because any linear combination of eigenvectors for the same eigenvalue is also an eigenvector for
Discrete_Fourier_transform
Concepts from linear algebra
In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by
Eigenvalues_and_eigenvectors
Mathematical optimization concept
This linear combination gives us an upper bound on the objective. The variables y of the dual LP are the coefficients of this linear combination. The
Dual_linear_program
Solutions of the Laplace equation in spherical polar coordinates
(again, up to the specific choice of normalization). By a simple linear combination of solid harmonics of ±m these functions are transformed into real
Solid_harmonics
Vector behavior under coordinate changes
{\displaystyle a_{j}^{i}} . Here, each vector Yj of the f′ basis is a linear combination of the vectors Xi of the f basis, so that Y j = ∑ i a j i X i , {\displaystyle
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Calculus property
any linear combination of functions equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation
Linearity_of_differentiation
Mathematical theorem in measure theory
every fixed linear combination of the coordinates of X n {\displaystyle {X}_{n}} converges in distribution to the correspondent linear combination of coordinates
Cramér–Wold_theorem
Type of polynomial used in Numerical Analysis
numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician
Bernstein_polynomial
Equation to approximate pooled degrees of freedom
calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees
Welch–Satterthwaite_equation
LINEAR COMBINATION
LINEAR COMBINATION
Girl/Female
Irish
Eimear possessed the “Six Gifts of Womanhood†– “beauty, a gentle voice, sweet words, wisdom, needlework and chastity!†She was bethrothed to the warrior Cuchulainn (read the legend) when they were children and they loved each other very deeply. But Cuchulainn had “a wandering eye†and Eimear endured this, realizing “everything new is fair,†but when he made love to Fand, wife of the sea god Manannan, Eimear confronted the lovers. After seeing the strength of Fand’s love she offered to withdraw. Touched by this display of unselfishness, Fand left Cuchulainn and returned to the sea. When Cuchulainn died Eimear spoke movingly and lovingly at his graveside.
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Boy/Male
Irish
Meaning “â€fair-haired,â€â€ the name has been popular since the sixth century when St. Finbar came to an area of Cork that was being tormented by a serpent. The people begged him to do something to help them. One night he went to where the serpent was sleeping and sprinkled it with holy water. The angry serpent tore and devoured the land until she slithered into the sea at Cork Harbor. The track she left behind filled with water and became the River Lee and that’s why St. Finbar is the patron saint of Cork. It is said that the sun didn’t set for two weeks after Finbar’s death.
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Surname or Lastname
English
English : metronymic from Line.
Female
English
English name probably derived from Germanic lindi, LINDA means "serpent."Â In some cases, it may have been derived from the Spanish word for "pretty."
Surname or Lastname
English (Cornish)
English (Cornish) : habitational name from a place named with Cornish lan ‘church’. In England this surname is now found chiefly in the southern counties of Wiltshire and Hampshire, and Berkshire; it has no doubt moved there from Cornwall.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Surname or Lastname
English
English : variant of Lanier 1.Dutch : variant of Leonard.Jewish (western Ashkenazic) : name taken by someone who was good at chanting the Pentateuch at public worship in the synagogue or who regularly did so, from West Yiddish layner ‘reader’ (a derivative of West Yiddish laynen ‘to read’, which comes ultimately from Latin legere ‘to read’).Jewish (Ashkenazic) : occupational name for a flax grower or merchant, from German Lein ‘flax’ + agent suffix -er.
Surname or Lastname
English (Devon; of Cornish origin)
English (Devon; of Cornish origin) : topographic name for someone who lived by a menhir, i.e. a tall standing stone erected in prehistoric times (Cornish men ‘stone’ + hir ‘long’).
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Boy/Male
Hindu
The Sun
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Boy/Male
Sikh
Love unending
Surname or Lastname
Swedish
Swedish : ornamental name from lind ‘lime tree’ + either the German suffix -er denoting an inhabitant, or the surname suffix -ér, derived from the Latin adjectival ending -er(i)us.English (mainly southeastern) : variant of Lind 2.German : habitational name from any of numerous places called Linden or Lindern, named with German Linden ‘lime trees’.
Boy/Male
Hindu
Lingam
LINEAR COMBINATION
LINEAR COMBINATION
Boy/Male
Hindu, Indian
An Ocean of Happiness
Male
French
French form of Roman Latin Aurelianus, AURELIEN means "golden."
Boy/Male
Indian, Punjabi, Sikh
Lord of Supreme
Girl/Female
Muslim/Islamic
Pure chaste
Girl/Female
Hindu
Well heard, A good reputation, Very famous
Female
Native American
Native American Choctaw unisex name ISI means "deer."
Boy/Male
Indian, Sanskrit, Tamil
Agreeable; Charming; Beloved
Girl/Female
Muslim/Islamic
Blessing of Allah
Boy/Male
Indian, Sanskrit
With No Desire
Boy/Male
British, English
Prince
LINEAR COMBINATION
LINEAR COMBINATION
LINEAR COMBINATION
LINEAR COMBINATION
LINEAR COMBINATION
n.
A vessel belonging to a regular line of packets; also, a line-of-battle ship; a ship of the line.
a.
Formed by right lines; rectilineal; as, a right-lined angle.
adv.
In a linear manner; with lines.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
n.
One who adjusts things to a line or lines or brings them into line.
n.
Made of linen; as, linen cloth; a linen stocking.
v. t.
To convert into vinegar; to make like vinegar; to render sour or sharp.
a.
Of a linear shape.
a.
Composed of lines; delineated; as, lineal designs.
n.
A dealer in linen; a linen draper.
n.
A lunar distance.
a.
Linear.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
prep. & adv.
Near.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
n.
One who lines, as, a liner of shoes.
v. t.
To mark with a line or lines; to cover with lines; as, to line a copy book.
n.
Alt. of Lingam
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.