An Etymological Dictionary of Astronomy and Astrophysics
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A procedure for finding the maximum or minimum of a → linear function where the → arguments are subject to linear → constraints. For problems involving more than two variables or problems involving a large number of constraints, solution methods used are those that are adaptable to computers. A well-known such → algorithm is the → simplex method.

→ linear; → programmings.

In statistics, a regression method that establishes a linear relationship between two random variables.

→ linear; → regression.

The real, physical size, as opposed to angular size.

→ linear; → size.

Physics: A → dynamical system whose evolution is a linear process. If a change in any variable at some initial time produces a change in the same or some other variable at some later time, twice as large a change at the same initial time will produce twice as large a change at the same later time.

→ linear; → system.

The rate of change of the position of an object that is traveling along a straight path. In other words, the velocity of an object when its moving direction is not changing. For a given → angular velocity (ω), the linear velocity v of the particle is directly proportional to the distance of the particle from the center of the circular path: v = ω ×r.

→ linear; → velocity.

The property, condition, or state of being linear.
Math.: A relationship between two variables so that when plotted on a graph they yield a straight line.

→ linear; → -ity.

A process of reduction to linear form by appropriate change of variables or by approximation.

Verbal noun of → linearize.

To make linear; give linear form to.

→ linear + → -ize.

A differential equation that has been derived from an original nonlinear equation.

Linearized, p.p. of → linearize; → differential; → equation.

In a manner characterized by first-degree algebraic terms.

Adverb of → linear.

A set of objects x₁, x₂, ..., x_n (→ vectors, → matrices, → polynomials, etc.) on a given set if there is a linear combination of them: a₁x₁ + a₂x₂ + ... + a_nx_n, which is zero, but at least one of the coefficients is non-zero. For example the binomials (2x + y) and (6x + 3y) are linearly dependent, since 3(2x + y) - (6x + 3y) = 0.

→ linearly; → dependent.

1) A set of objects x₁, x₂, ..., x_n (→ vectors, → matrices, → polynomials, etc.) if it si not → linearly dependent.
2) Of two particular solutions (y₁, y₂) of a → homogeneous linear differential equation of the second order (y^'' + a₁ y^' + a₂y = 0) on an interval [a, b], if their ratio in this interval is not a constant: y₁/y₂≠ constant.

→ linearly; → independent.

Light exhibiting → linear polarization.

→ linearly; → polarized; → light.

A → linear differential equation if Q(x)≠ 0 on interval I.

→ nonhomogeneous; → linear; → differential; → equation.

Not a linear function of the relevant variables.
Containing a variable with an exponent other than one; opposite of → linear.

→ non-; → linear.

An electronic device whose output is not directly proportional to its input. For example, in a → diode the current is a nonlinear function of the voltage; its voltage-current characteristics do not obey → Ohm's law.

→ nonlinear; → device.

Same as → chaos.

→ nonlinear; → dynamics.

The instability of a physical or mathematical system that arises from the nonlinear nature of relevant variables and their interactions within the system.

→ nonlinear; → instability.

A system in which small changes can result in large effects, and large changes in small effects.

→ nonlinear; → system.

The property, condition, or state of being → nonlinear.

→ non-; → linearity.