linear

1. 1
   adjective

   Shaped like a line (straight or nearly straight) and following a direct course.

   The architect favored linear forms, with long straight corridors and unbroken edges.

   The procession kept to a strictly linear route down the main avenue.

   Similarstraight, direct

   Oppositecurved, winding

   Note

   The plainest sense, and the one the word's shape spells out: Latin līneāris, built on līnea, "line". In use it is looser than straight. A survey route can be linear without being a perfectly straight line, so long as it keeps one consistent course. The word describes a direction held, not a geometry perfected. Say straight when you mean it exactly.

2. 2
   adjective

   Relating to or concerned with lines.

   The diagram relied on linear elements to connect each node.

   Her drawing emphasized linear detail rather than shaded mass.

   Similarlineal

   Note

   A sense with a twin. Lineal came from the same Latin word by a separate road into English and can stand in for it here. Linear is still the everyday choice for things made of or concerned with lines, such as the linear detail of a drawing or the linear elements of a diagram. Lineal sounds markedly bookish beside it.

3. 3
   adjective

   Made or meant to be used in a step-by-step, sequential way.

   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.

   Similarsequential, chronological, consecutive

   Oppositenonlinear

4. 4
   adjective

   Long and narrow in shape, with margins that run nearly parallel: a common description of leaves.

   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.

   Note

   Grass blades and many conifer needles are the model cases. Botanists use the word for a leaf several times longer than it is wide, whose margins stay essentially parallel for most of their length. In a formal plant description it is a fixed shape term, so a leaf that tapers noticeably or swells in the middle does not qualify, however slender it looks.

5. 5
   adjective

   Describing a measurement of length along a single spatial dimension, rather than area or volume.

   The contractor quoted the new railing by the linear foot.

   Fabric shops often sell trim by the linear yard instead of by area.

   Similarrunning

   Note

   A linear meter is simply a meter. The adjective is there to stress that only length counts, as against square meters of area or cubic meters of volume. Trades use it when a material could be measured either way, such as trim, railing or fabric, so the customer knows the price runs along the length, not across the surface.

6. 6
   adjective

   Of a polynomial or equation, having degree one, built only from variables raised to the first power, plus a constant.

   Every linear function has a constant rate of change.

   Students graph linear expressions before they tackle quadratics.

   Oppositenonlinear

   Note

   Degree one is stricter than it looks. Each variable must appear to the first power and on its own. So 4x + 5y + ½z qualifies, but 4xy + ½z does not, because the product xy counts as degree two even though neither letter carries an exponent. A squared term such as z² rules an expression out just as plainly.

7. 7
   adjective

   Of an equation or system, involving only linear polynomials, with no variable raised above the first power.

   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.

   Oppositenonlinear

   Note

   The name leads back to the "straight line" meaning. The graph of y = ax + b is a straight line with slope a and y-intercept b. With more unknowns, the solutions form a plane or a higher-dimensional flat. Systems of such equations are the central business of elimination methods in linear algebra.

8. 8
   adjective

   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).

   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.

   Oppositenonlinear

   Note

   Here the word tightens. A linear map must send zero to zero, since f(0·v) = 0·f(v). So y = ax + b, though linear as an equation, is not a linear map unless b is zero. Mathematicians name the field of scalars when it matters, as in a K-linear or ℝ-linear map. Once bases are fixed, every such map is represented by a matrix.

9. 9
   adjective

   Of broadcasting, delivered on a fixed schedule rather than on demand.

   Advertisers are shifting budgets away from linear television toward streaming platforms.

   The broadcaster kept its linear schedule while launching an on-demand app.

   Similarbroadcast

   Oppositestreaming

   Note

   The broadcast cousin of the "step-by-step" meaning: a linear channel runs in one sequence the audience cannot reorder. It pairs with TV, radio, video and content, and its opposites are streaming, on-demand and non-linear. Wolfgang Hoeg and Thomas Lauterbach's Digital Audio Broadcasting (2004) already set linear, tune-in radio against non-linear listening to stored audio. Industry writing often uses it with a note of decline.

10. 10
    adjective

    Of a map, being a module homomorphism: a homomorphism of additive groups that also commutes with scalar multiplication.

    The map is linear, preserving both addition and the action of each scalar.

    Module theory studies linear maps between modules over a fixed ring.

    Note

    The same word carried from vector spaces to modules over a ring. The map must respect addition and commute with the ring's scalars, so f(r·x) = r·f(x). It generalizes maps between vector spaces: a vector space is simply the case where the ring happens to be a field, and there the two definitions coincide.

11. 11
    nounslangabbreviationellipsis

    Ellipsis of linear amplifier.

    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.

    Note

    Radio operators' shorthand: the adjective is kept and the noun dropped, so a linear is the amplifier itself, and the plural is linears. The name records what the circuit does, since its output stays proportional to its input while delivering more power. Among amateur operators it is ordinary talk. In a manual or formal notice, write linear amplifier in full.

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