linear

Expressed in point-slope form, a linear equation in two dimensions may be written as y - y₁ = m(x - x₁), where m is again the slope of the line, and (x₁, y₁) is a point in the line.

In Mathematics, the adjective "linear" is used in two main senses:

1. A function φ on a vector space V over a field F is called linear iff:
   • ∀x,y∈V: φ(x+y)=φ(x)+φ(y)
   • ∀x∈V,a∈F: φ(a*x)=a*φ(x).
   For a function over the field R, the second condition will follow if φ is also known to be continuous.

   I've intentionally said nothing about the range of φ. When the range is F, φ is a linear functional; when it is another vector space W, φ is a linear transformation. The adjective might be applied in other situations (even when not working on a vector space!), too. For instance, a little-known fact is that perimeter is linear for convex shapes in R²!

2. Confusingly, a function l:R->R^k is also called "linear" if it describes a straight line: l(x)=x*a+b.

When b!=0, l is NOT "linear" in the first sense! It would more properly be called an affine function. Unfortunately we're stuck with the older name.

Each night, LINEAR searches about 8% of the visible sky several times. Each image is then compared to identify any perceptible changes each point of light (potential near earth asteroid). These objects are close enough that the parallax of the earth moving, and the actual motion of the object would be detected.

Many comets have been discovered by LINEAR, a small sample of comets that are visible in 2002:

• C/2001 HT50 (LINEAR-NEAT): perihelion of 2.8 AU on July 8, 2003
• C/2001 N2 (LINEAR): perihelion of 2.7 on August 19, 2002
• C/2001 RX14 (LINEAR): perihelion of 2.06 AU on January 18, 2002

Of LINEAR's discovery, probably the most well known was C/1999 S4 (LINEAR) which was well observed and photographed by ground based and space based telescopes.

http://www.ll.mit.edu/LINEAR/
http://neo.jpl.nasa.gov/missions/linear.html
http://www.meteors.com/comet_info.html

Lin"e*ar (?), a. [L. linearis, linearius , fr. linea line: cf. F. lin'eaire. See 3d Line.]

1.

Of or pertaining to a line; consisting of lines; in a straight direction; lineal.

2. Bot.

Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.

Linear differential Math., an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients. -- Linear equation Math., an equation of the first degree between two variables; -- so called because every such equation may be considered as representing a right line. -- Linear measure, the measurement of length. -- Linear numbers Math., such numbers as have relation to length only: such is a number which represents one side of a plane figure. If the plane figure is square, the linear figure is called a root. -- Linear problem Geom., a problem which may be solved geometrically by the use of right lines alone. -- Linear transformation Alg., a change of variables where each variable is replaced by a function of the first degree in the new variable.

© Webster 1913.