# linear

Pronunciation: US say "LIN-ee-ur" /ˈlɪni.əɹ/; UK say "LIN-ee-uh" /ˈlɪni.ə/

## Adjective

1. Shaped like a line (straight or nearly straight) and following a direct course.
   - Simple: Shaped like a straight line, or going in a straight, direct direction.
   - _The architect favored linear forms, with long straight corridors and unbroken edges._
   - _The procession kept to a strictly linear route down the main avenue._
2. Relating to or concerned with lines.
   - Simple: Having to do with lines, or connected with lines.
   - _The diagram relied on linear elements to connect each node._
   - _Her drawing emphasized linear detail rather than shaded mass._
3. Made or meant to be used in a step-by-step, sequential way.
   - Simple: Done or used in a set order, one step after another.
   - _The course follows a linear structure, each lesson building on the one before._
   - _Some readers dislike the novel's strictly linear plot, which never jumps in time._
4. Long and narrow in shape, with margins that run nearly parallel: a common description of leaves.
   - Simple: Long, thin, and narrow, with sides that are almost parallel.
   - _Botanists noted the fern's linear leaflets, each many times longer than wide._
   - _The iris sends up tall, linear leaves with edges that stay nearly parallel._
5. Describing a measurement of length along a single spatial dimension, rather than area or volume.
   - Simple: Measuring length in just one direction, not area or space.
   - _The contractor quoted the new railing by the linear foot._
   - _Fabric shops often sell trim by the linear yard instead of by area._
6. Of a polynomial or equation, having degree one, built only from variables raised to the first power, plus a constant.
   - Simple: Using variables with no powers higher than one, so the graph forms a straight line.
   - _Every linear function has a constant rate of change._
   - _Students graph linear expressions before they tackle quadratics._
7. Of an equation or system, involving only linear polynomials, with no variable raised above the first power.
   - Simple: Made up only of straight-line terms, with no higher powers.
   - _Engineers reduced the model to a set of linear equations they could solve quickly._
   - _A linear system in three unknowns may have one solution, none, or infinitely many._
8. Of a function, additive and homogeneous: it distributes over vector addition and respects scalar multiplication, so f(v+w) = f(v)+f(w) and f(cv) = cf(v).
   - Simple: Describing a function that adds inputs and scales them in a steady, predictable way.
   - _Differentiation is a linear map, since the derivative of a sum is the sum of the derivatives._
   - _Every linear transformation of the plane can be captured by a matrix._
9. Of broadcasting, delivered on a fixed schedule rather than on demand.
   - Simple: Shown on a set schedule, not whenever you choose to watch.
   - _Advertisers are shifting budgets away from linear television toward streaming platforms._
   - _The broadcaster kept its linear schedule while launching an on-demand app._
10. Of a map, being a module homomorphism: a homomorphism of additive groups that also commutes with scalar multiplication.
   - Simple: Describing a map between two number systems that keeps adding and scaling the same.
   - _The map is linear, preserving both addition and the action of each scalar._
   - _Module theory studies linear maps between modules over a fixed ring._

## Noun

11. Ellipsis of linear amplifier. *(slang)* — Ellipsis of linear amplifier.
   - Simple: Short for linear amplifier. Ham radio operators use it for the unit that boosts transmit power.
   - _After upgrading to a linear, he finally worked stations all the way to Japan._
   - _The club reminded members to keep their linear within the legal power limit._

## Origin

Borrowed from Latin līneāris, from līnea ("line") plus the adjective-forming suffix -āris. It is a doublet of lineal.

Source: DictionaryAI, https://dictionaryai.com/define/linear (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).