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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
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
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
Linear map or polynomial function of degree one
linear function Linear approximation Linear interpolation Discontinuous linear map Linear least squares "The term linear function means a linear form
Linear_function
On algebraic independence of logarithms
discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. Nearly fifteen years earlier
Baker's_theorem
Syllabic script used for writing Mycenaean Greek
contains Linear B Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear B. Linear B is
Linear_B
Equation that does not involve powers or products of variables
In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0
Linear_equation
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
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
Scalar-valued bilinear function
which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w)
Bilinear_form
Method to solve optimization problems
smallest) value if such a point exists. Linear programs are problems that can be expressed in standard form as: Find a vector x that maximizes c T x
Linear_programming
a binary form is a polynomial in the coefficients of a binary form in two variables x and y that remains invariant under the special linear group acting
Invariant_of_a_binary_form
{\displaystyle f} be a linear form on M . {\displaystyle M.} Then f {\displaystyle f} has an extension to a continuous positive linear form on X {\displaystyle
Positive_linear_functional
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
Polynomial with all terms of degree two
it is isotropic. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal
Quadratic_form
Theorem related to ordinary least squares
estimator across samples) within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances
Gauss–Markov_theorem
Polynomial whose nonzero terms all have the same degree
form of degree 1 is a linear form. A form of degree 2 is a quadratic form. In geometry, the Euclidean distance is the square root of a quadratic form
Homogeneous_polynomial
Types of mappings in mathematics
subfield (and sometimes even the author). In linear algebra, it is synonymous with a linear form, which is a linear mapping from a vector space V {\displaystyle
Functional_(mathematics)
Chemical compound
are known: a linear form with double bonds and charge transfer, and a cyclic form. Both forms are highly unstable, though the linear form is the more stable
Trinitrogen
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
5-Carbon simple sugar
exist in two forms, open-chain (linear) or closed-chain (cyclic), that easily convert into each other in water solutions. The linear form of a pentose
Pentose
6-carbon simple sugar
aldohexoses are a subclass of the hexoses which, in the linear form, have the carbonyl at carbon 1, forming an aldehyde derivative with structure H−C(=O)−(CHOH)5−H
Hexose
Matrix form in linear algebra
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just
Hermite_normal_form
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
bilinear form On vector space V over field K, a bilinear form is a function B : V × V → K {\displaystyle B:V\times V\to K} that is linear in each variable
Glossary_of_linear_algebra
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
Possible form of a matrix
In linear algebra, a matrix is in row echelon form if it can be obtained as the result of Gaussian elimination. Every matrix can be put in row echelon
Row_echelon_form
Group of simple sugar and carbohydrate compounds
with molecular formula C5H10O5 and the linear-form composition H−(C=O)−(CHOH)4−H. The naturally occurring form, d-ribose, is a component of the ribonucleotides
Ribose
Generalised alphabetical order
\mathbb {R} ^{n},} which is injective if the forms are linearly independent (it may be also injective if the forms are dependent, see below). The lexicographic
Lexicographic_order
Class of statistical models
generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model
Generalized_linear_model
Generalized function whose value is zero everywhere except at zero
Schwartz 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
Dirac_delta_function
Sum of terms, each multiplied with a scalar
results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations
Linear_combination
Method of curve fitting
In mathematics, linear interpolation (sometimes lerp) is a method of curve fitting using linear polynomials to construct new data points within the range
Linear_interpolation
Lack of tooth enamel
categorized by shape or location. Common categories are pit-form, plane-form, linear-form, and localised enamel hypoplasia. Hypoplastic lesions are found
Enamel_hypoplasia
Statistical modeling method
conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution
Linear_regression
Chemical compound
also exists in the condensed state when formed by superacids. In the ground state, HC+NH is a simple linear molecule, whereas its excited triplet state
Protonated_hydrogen_cyanide
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 mathematical measure
by the Riesz–Markov–Kakutani representation theorem, each positive linear form on K(X) arises as integration with respect to a unique regular Borel
Radon_measure
Type of transport infrastructure
because they carry so many people, creating linear agglomerations like the Las Vegas Strip or the linear form of many neighborhood retail areas. A 2019
Transport_corridor
In mathematics, vector space of linear forms
corresponding dual vector space (or just dual space for short) consisting of all linear forms on V , {\displaystyle V,} together with the vector space structure of
Dual_space
Notation for quantum states
the form ⟨ f | {\displaystyle \langle f|} . Mathematically it denotes a linear form f : V → C {\displaystyle f:V\to \mathbb {C} } , i.e. a linear map
Bra–ket_notation
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
Map from multiple vectors to an underlying field of scalars, linear in each argument
separately K {\displaystyle K} -linear in each of its k {\displaystyle k} arguments. More generally, one can define multilinear forms on a module over a commutative
Multilinear_form
Statistical technique
PCR is a form of reduced rank regression. More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression
Principal component regression
Principal_component_regression
On transcendence of certain numbers
β = 0 {\displaystyle b\ln {\alpha }+\ln {\beta }=0} of the general linear form in logarithms, which was studied by Gelfond[citation needed] and then
Hilbert's_seventh_problem
Narrative technique
utilizes a non-linear structure, focusing on events throughout the life of the titular character rather than describing them in a linear narrative. From
Nonlinear_narrative
Topics referred to by the same term
up linear in Wiktionary, the free dictionary. Linearity is a property of various things in mathematics, physics, and electronics. Linear, linearly, or
Linear_(disambiguation)
Algebraic object with geometric applications
from V to its double dual, given by evaluating a linear form in V∗ against a vector in V. This linear mapping is an isomorphism in finite dimensions, and
Tensor
linear chromosome is a chromosome which is linear in shape, and contains terminal ends. In most eukaryotic cells, DNA is arranged in multiple linear chromosomes
Linear_chromosome
Differential equation that is linear with respect to the unknown function
linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form a
Linear_differential_equation
Topics referred to by the same term
V × V → F that is linear in both arguments Differential form, a concept from differential topology that combines multilinear forms and smooth functions
Form
Concept in mathematical invariant theory
form of even degree is a polynomial in its coefficients that vanishes when the form is a sum of an unusually small number of powers of linear forms.
Catalecticant
which is the rate about which the linear form above is obtained as a first-order approximation of the non-linear model. At any other desired target for
Divine_coincidence
Chemical group (–C3H7) derived from propane
alkyl substituent with chemical formula −CH2CH2CH3 for the linear form. This substituent form is obtained by removing one hydrogen atom attached to the
Propyl_group
Concept in linear algebra
specifically linear algebra, a degenerate bilinear form f ( x , y ) {\displaystyle f(x,y)} on a vector space V {\displaystyle V} is a bilinear form such that
Degenerate_bilinear_form
Concept in mathematics
infinite-dimensional), and assume T {\displaystyle T} is a linear function from V {\displaystyle V} to the field (a linear form). Then the function defined by B ( x , y
Symmetric_bilinear_form
Bilateral trade flow model
countries that are being measured. The equation can be changed into a linear form for the purpose of econometric analyses by employing logarithms. The
Gravity_model_of_trade
American semiconductor manufacturer
2010-08-25. "LINEAR TECHNOLOGY CORP /CA/ 2015 Annual Report Form (10-K)" (XBRL). United States Securities and Exchange Commission. August 19, 2015. "LINEAR TECHNOLOGY
Linear_Technology
Articulated mechanical linear actuator that becomes rigid under compression loading
as a linear chain actuator, push-pull chain actuator, electric chain actuator or column-forming chain actuator, is a specialized mechanical linear actuator
Rigid_chain_actuator
Dimension of the column space of a matrix
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number
Rank_(linear_algebra)
Electric motor that produces a linear force
A linear motor is an electric motor that has had its stator and rotor "unrolled", thus it produces a linear force along its length, rather than a rotational
Linear_motor
Amount of reducing sugars in a sugar product
chain ends with a reducing sugar, containing a free aldehyde in its linear form. As the starch is hydrolysed, the molecules become shorter and more reducing
Dextrose_equivalent
Actuator that creates motion in a straight line
A linear actuator is an actuator that creates linear motion (i.e., in a straight line), in contrast to the circular motion of a conventional electric motor
Linear_actuator
Chemical compound
acetone. Linear polyethylenimine has a melting point of around 67 °C. Both linear and branched polyethylenimine can be stored at room temperature. Linear polyethylenimine
Polyethylenimine
Type of village
A linear settlement is a (normally small to medium-sized) settlement or group of buildings that are formed in a long line. Many of these settlements are
Linear_settlement
Type of organic molecule with a linear structure
alkenes, have both linear and ring isomers, that is, both acyclic and cyclic. For those with 4 or more carbons, the linear forms can have straight-chain
Open-chain_compound
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
distinct. In linear algebra, a Jordan normal form, also known as a Jordan canonical form, is an upper triangular matrix of a particular form called a Jordan
Jordan_normal_form
Open conjecture in multiplicative Diophantine approximation
d\geq 3} linearly independent real linear forms in d {\displaystyle d} variables. If L {\displaystyle L} is not a nonzero constant multiple of a form with
Littlewood_conjecture
ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. Since it is equivalent to another lemmas used in optimization
Finsler's_lemma
Tool for precise linear motion
platform and a base, joined by some form of guide or linear bearing in such a way that the platform is restricted to linear motion with respect to the base
Linear_stage
Theorem in mathematical statistics
distribution (the Gaussian distribution) by the independence of two linear forms of n {\displaystyle n} independent random variables. The theorem was
Darmois–Skitovich_theorem
Defunct pro audio manufacturer mainly known for its power amps
Phase Linear was an audio equipment manufacturer founded by Bob Carver and Steve Johnston in 1970. While primarily known as a power amplifier company it
Phase_Linear
Relation between temperature and the equilibrium constant of a chemical reaction
constant, the preceding equation gives ln K as a linear function of 1/T and hence is known as the linear form of the Van 't Hoff equation. Therefore, when
Van_'t_Hoff_equation
Graph of enzyme kinetics
the alternative linear forms of the Michaelis–Menten equation such as the Hanes–Woolf plot or Eadie–Hofstee plot, all linearized forms of the Michaelis–Menten
Lineweaver–Burk_plot
Group of 𝑛 × 𝑛 invertible matrices
In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with
General_linear_group
English mathematician (1939–2018)
until his death. His interests were in number theory, transcendence, linear forms in logarithms, effective methods, Diophantine geometry and Diophantine
Alan_Baker_(mathematician)
Method for estimating the unknown parameters in a linear regression model
ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of
Ordinary_least_squares
Mathematical concept
symplectic bilinear form. A symplectic bilinear form is a mapping ω : V × V → F {\displaystyle \omega :V\times V\to F} that is Bilinear Linear in each argument
Symplectic_vector_space
Chemical compound
contain, in addition to the linear form, branched and cyclic polyamines. As an amine, it is an organic base and can form ammonium salts by reaction with
Pentaethylenehexamine
the Witten zeta function of S U ( 3 ) {\displaystyle SU(3)} but the linear form x + 1 {\displaystyle x+1} has y {\displaystyle y} -coefficient equal
Shintani_zeta_function
Polyphonic music with separate melodies
idiosyncratic modifications in the rules. Many of Fux's rules concerning the purely linear construction of melodies have their origin in solfeggio. Concerning the
Counterpoint
Electronic circuits obeying the superposition principle
A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit F(x) when a linear combination
Linear_circuit
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
Concept in computing
a linear form, while still retaining multiple references to it. Uniqueness guarantees that a value has no other references to it, while linearity guarantees
Uniqueness_type
Chemical compound
recombination pathway is dominant by 30%; however, the HCNH+ must be in its linear form. Dissociative recombination with its structural isomer, H2NC+, exclusively
Hydrogen_cyanide
Form of cryptanalysis
In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have
Linear_cryptanalysis
Graph where every edge is in one triangle
matching. Locally linear graphs have also been called locally matched graphs. More technically, the triangles of any locally linear graph form the hyperedges
Locally_linear_graph
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
Writing system from Elam
Linear Elamite was a writing system used in Elam during the Bronze Age between c. 2300 and 1850 BCE, and known mainly from a few extant monumental inscriptions
Linear_Elamite
Matrix operation which flips a matrix over its diagonal
In linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the
Transpose
Non-linear media is a form of audiovisual media that can be interacted with by the viewer, such as by selecting television shows to watch through a video
Non-linear_media
Two special types of linear grammars are the following: the left-linear or left-regular grammars, in which all rules are of the form A → αw where α is either
Linear_grammar
Type of voltage regulator
In electronics, a linear regulator is a voltage regulator used to maintain a steady voltage. The resistance of the regulator varies in accordance with
Linear_regulator
Type of sensor
A linear encoder is a sensor, transducer or readhead paired with a scale that encodes position. The sensor reads the scale in order to convert the encoded
Linear_encoder
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
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 concept in polynomial theory
into a product of linear forms. If α 1 u 1 + … + α n u n {\displaystyle \alpha _{1}u_{1}+\ldots +\alpha _{n}u_{n}} is such a linear factor, then α 1
Resultant
multi-degree d 1 , … , d k {\displaystyle d_{1},\ldots ,d_{k}} by the linear form d = d 1 t 1 + ⋯ + d k t k . {\displaystyle \mathbf {d} =d_{1}t_{1}+\cdots
Multi-homogeneous Bézout theorem
Multi-homogeneous_Bézout_theorem
Graph drawn with all edges intersecting
any given set of points as vertices is to form an edge between each farthest pair of points. For a linear thrackle, each connected component contains
Thrackle
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
LINEAR FORM
LINEAR FORM
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
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
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
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
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.
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.
Boy/Male
Hindu
Lingam
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
English : metronymic from Line.
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 : occupational name for a refiner of gold and other metals, from Middle English fine(n) ‘to refine or purify’ (a derivative of fine ‘fine’, ‘pure’).Probably a translated form of German Feiner.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Girl/Female
Irish
Irish form of Jane “God is gracious.â€
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’.
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’.
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
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
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
LINEAR FORM
LINEAR FORM
Surname or Lastname
English
English : unexplained.Southern Italian : from a short form of the personal names Boncore, literally ‘good heart’, a medieval omen name, or Belcore.
Girl/Female
Hindu
Sacred, Dignified
Girl/Female
Indian, Punjabi, Sikh
Destroyer of Tyranny
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Blessing; Offering to God During Pooja; Devotional Offering
Boy/Male
American, Anglo, British, Chinese, Christian, Danish, Dutch, English, French, German, Irish, Swedish
Prosperous Friend; Valued; Wealthy Friend; Blessed Friend; Rich Friend
Girl/Female
English, Italian
Flower
Surname or Lastname
English
English : habitational name from Bridgwater in Somerset; the water which the bridge at Bridgwater crosses is the Parrett river, but the place name actually derives from Brigewaltier, i.e. ‘Walter’s bridge’, after Walter de Dowai, the 12th-century owner.
Boy/Male
Tamil
Diamond
Boy/Male
Indian
Morning
Female
English
Variant spelling of English Nora, NORAH means "honor, valor."
LINEAR FORM
LINEAR FORM
LINEAR FORM
LINEAR FORM
LINEAR FORM
v. t.
To convert into vinegar; to make like vinegar; to render sour or sharp.
n.
A vessel belonging to a regular line of packets; also, a line-of-battle ship; a ship of the line.
n.
A dealer in linen; a linen draper.
a.
Linear.
a.
Composed of lines; delineated; as, lineal designs.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
a.
Formed by right lines; rectilineal; as, a right-lined angle.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
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 lines, as, a liner of shoes.
n.
Alt. of Lingam
adv.
In a linear manner; with lines.
v. t.
To mark with a line or lines; to cover with lines; as, to line a copy book.
n.
A lunar distance.
prep. & adv.
Near.
a.
Of a linear shape.
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.