# Linear

## Meanings and phrases

adj.

- designating or involving an equation whose terms are of the first degree; additive
- of or in or along or relating to a line; involving a single dimension; one-dimensional
- of a circuit or device having an output that is proportional to the input; analogue; analog
- (of a leaf shape) long and narrow; elongate
- measured lengthwise; running

n.

- an undeciphered writing system used in Crete in the 17th century B.C.

n.

- a syllabic script used in Greece in the 13th century B.C.

n.

- ions are accelerated along a linear path by voltage differences on electrodes along the path; linac

n.

- the part of algebra that deals with the theory of linear equations and linear transformation

- The domain studying these matters is called numerical linear algebra.
- An example of an external binary operation is scalar multiplication in linear algebra.
- Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.

n.

- a polynomial equation of the first degree

n.

- a long slender leaf; elongate leaf

n.

- a unit of measurement of length; linear unit

n.

- an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)

- This defines another bounded linear operator , the adjoint of .
- A linear operator is a map that inputs a ket and outputs a ket.
- In other words, if is a linear operator and is a ket, then is another ket.

n.

- the appearance of things relative to one another as determined by their distance from the viewer; perspective

n.

- a mathematical technique used in economics; finds the maximum or minimum of linear functions in many variables subject to constraints

- Mathematical models also include those in game theory, linear programming, and econometrics.
- In applied economics, input-output models employing linear programming methods are quite common.
- In 1984, Karmarkar's algorithm for linear programming was developed by mathematician Narendra Karmarkar.

n.

- the relation between variables when the regression equation is linear: e.g., y = ax + b; rectilinear regression

- (2008) discusses this for clustered errors in linear regression.
- A basic tool for econometrics is the multiple linear regression model.

n.

- a unit of measurement of length; linear measure

n.

- a linear unit of distance in metric terms

n.

- linear accelerator that uses microwaves

n.

- a linear unit of distance used in navigation

E.g.

- ", moving in a linear combination of up and forward.
- a linear combination as a weighted sum) of basis states.
- The Lie bracket of pairs of generators is a linear combination of generators from the set, i.e.

E.g.

- Such a factorisation can be found in linear time.
- A linear time dependence was incorrectly assumed.
- Additionally, acyclic FSAs can be minimized in linear time.

E.g.

- Another way of solving the same system of linear equations is by substitution.
- The simplest equations to solve are linear equations that have only one variable.
- Another application of matrices is in the solution of systems of linear equations.

E.g.

- See also general linear group over finite fields.
- The group "N" is known as the special linear group SL(3).
- Thus, the set of such matrices (of fixed size "n") form a group known as the special linear group.

E.g.

- A rotation of axes is a linear map and a rigid transformation.
- The map is a linear map from to .
- If is a linear map, then the "transpose" (or "dual") is defined by for every .

E.g.

- A linear system will have no tune shift with amplitude.
- A linear system that is not time-invariant can be solved using other approaches such as the Green function method.
- However, even in a linear system in which the power quantity is the product of two linearly related quantities (e.g.

E.g.

- See also general linear group over finite fields.
- ANOVA is considered to be a special case of linear regression which in turn is a special case of the general linear model.
- The group of units is denoted by GL(2,"R"), adopting notation from the general linear group, where "R" is usually taken to be a field.

E.g.

- As re-defined in 2006, TDB is a linear transformation of TCB.
- In particular, is a linear transformation up to a small error term.
- In the limit as v and w tend to zero, it must therefore be a linear transformation.

E.g.

- Compound and adjugate matrices appear when computing determinants of linear combinations of matrices.
- An interesting question is whether there are other additive polynomials except these linear combinations.
- Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals.

E.g.

- In case of linear function, "at no point is there an attempt to show that the equation's graph really is a line.
- Linear phase Linear phase is a property of a filter, where the phase response of the filter is a linear function of frequency.
- The simplest case, apart from the trivial case of a constant function, is when is a linear function of , meaning that the graph of is a line.

E.g.

- ANOVA is considered to be a special case of linear regression which in turn is a special case of the general linear model.
- The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks.
- It is a kind of hierarchical linear model, which assumes that the data being analysed are drawn from a hierarchy of different populations whose differences relate to that hierarchy.

E.g.

- It has two to four linear leaves, 7–15 cm long.
- It has narrow linear leaves, which are white-woolly beneath.
- Between three and five linear leaves emerge at the base, each leaf long and wide.

E.g.

- The village itself is a linear village with roughly 13 houses.
- It is a linear village with individual houses and farms all along the main road.
- Sessay Sessay is a small, linear village and civil parish in North Yorkshire, England.

E.g.

- The leaves are linear and greyish green, and up to long.
- The leaves are linear to almost cylindrical, long and wide.
- The leaves are linear, 20–40 cm long.

E.g.

- The railway is separated from the linear park by a stout safety fence.
- The Ward River Valley Park is a large linear park on the banks of the Ward River.
- It forms what trail managers, Northamptonshire County Council, describe as a linear park.

E.g.

- The petals are a linear in shape and similar in size to the sepals.
- The dorsal sepal is erect, linear in shape, long, wide with a pointed end.
- The leaves are 5 to 15 centimeters long and linear in shape with lobes near the ends.

E.g.

- Another way of solving the same system of linear equations is by substitution.
- Near the northern and southern inner walls is a system of linear rilles in the surface.
- In 1986 Baron and Kenny introduced principles for detecting and evaluating mediation in a system of linear equations.

E.g.

- Such a row acts on R as a linear functional by ordinary matrix multiplication.
- Let formula_166 be the linear functional on formula_167 given by formula_168 for formula_169.
- For every vector in a Hilbert space , the mapping defines a continuous linear functional on .

E.g.

- Euler's notation is useful for stating and solving linear differential equations.
- Other examples are solutions of linear differential equations with polynomial coefficients.
- A linear differential equation with constant coefficients is transformed into an easily solvable algebraic equation.

E.g.

- In general, a linear relationship between two second-order tensors is a fourth-order tensor.
- This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named.
- The linear relationship between the MSD and time "t" allows for graphical methods to determine the diffusivity constant "D".

E.g.

- Eukaryotic genomes are composed of one or more linear DNA chromosomes.
- The second series followed a more linear structure, although it retained the stand-up sequences.
- However, a firefight had been anticipated and the French infantry had accordingly advanced in more linear formation.