linear

Etymology

From Latin līneāris, from līnea (“line”) + -āris (adjectival suffix). Doublet of lineal.

adj

1. Having the form of a line; straight or roughly straight; following a direct course.
   The route taken does not have to be a perfectly straight line, just so long as it is linear and is followed consistently for each transect taken. 2019, Li Huang, James Lambert, “Another Arrow for the Quiver: A New Methodology for Multilingual Researchers”, in Journal of Multilingual and Multicultural Development, →DOI, page 4
2. Of or relating to lines.
3. Made, or designed to be used, in a step-by-step, sequential manner.
   a linear medium
4. (botany, of leaves) Long and narrow, with nearly parallel sides.
5. (mathematics) (of polynomials or polynomial equations)
   1. (of a polynomial) Having degree less than one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n, where each x_i is a variable and each a_i is a coefficient. See also Linear polynomials on Wikipedia.Wikipedia
      {{ux|en|4x+5y+1/2z is a linear polynomial, but 4xy+1/2z and 4x+z² are not.}}
   2. (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia
      The graph of the linear equation y=ax+b is a straight line with slope a and y-intercept b
6. (mathematics) (of functions or maps)
   1. (of a function">function between vector spaces) An additive, homogeneous mapping; that is, a function">function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also Linear Map on Wikipedia.Wikipedia
      The map f:ℝ³→ℝ² taking (x,y,z)↦(x+y+z,x-y+3z) is a linear map.
   2. (of a function">function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
7. (physics) A type of length measurement involving only one spatial dimension (as opposed to area or volume).
   a linear meter

noun

1. (radio slang) Ellipsis of linear amplifier..