coefficient

Dictionary: co·ef·fi·cient (kō'ə-fĭsh'ənt) pronunciation

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term, as 4 in the term 4x, or x in the term x(a + b).
A numerical measure of a physical or chemical property that is constant for a system under specified conditions such as the coefficient of friction.

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A factor that measures a specific property of a given substance and isconstant for that substance under specific conditions.

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1. an expression of the change or effect produced by the variation in certain factors, or of the ratio between two different quantities.
2. in chemistry, a number or figure put before a chemical formula to indicate how many times the formula is to be multiplied.

absorption c. — 1. the fraction of a beam of radiation that is absorbed in passing through a unit length of absorbing material.
alienation c. — a measure of the lack of association between two variables. Called also the coefficient of nondetermination.
Bunsen c. — see absorption coefficient (2) (above).
contingency c. — a measure of association between qualitative assessments of two variables.
correlation c. — a measure of association which indicates the degree to which two or more sets of observations fit a linear relationship. Denoted by ‘r’, it can vary from −1.0 to 1.0.
determination c. — the coefficient of determination is the square of the correlation coefficient (r²). It describes the proportion of the variation of one of the correlated variables, explainable by the variation of the other variable. The value of the coefficient must lie between 0 and 1.
digestibility c. — percentage of the food ingested that is absorbed.
disarray c. — the measure of the degree of discord between two variables.
friction c. — the effect that the material in a surface has on the frictional force created by the application of a force to the surface: S = f × N, where S = friction, f = friction coefficient, N = reaction to the vertical application of a given force. In a normal joint the f value is very small (0.008).
c. of nondetermination — see alienation coefficient.

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IN BRIEF: A factor that contributes to produce a result.

Coefficient is a mathematical term often used in calculus.

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For other uses of this word, see coefficient (disambiguation).

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Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (June 2009)

In mathematics, a coefficient is a constant multiplicative factor of a specific object. For example, in the expression 9x², the coefficient of x² is 9.

The object can be such things as a variable, a vector, a function, etc. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as:

$a_1 x_1 + a_2 x_2 + a_3 x_3 + \cdots$

where a_n is the coefficient of the variable x_n for each n = 1, 2, 3, …

In a polynomial P(x) of one variable x, the coefficient of x^k can be indexed by k, giving the convention that for example:

$P(x) = a_k x^k + \cdots + a_1 x^1 + a_0.$

For the largest k where a_k ≠ 0, a_k is called the leading coefficient of P because most often, polynomials are written starting from the left with the largest power of x. So for example the leading coefficient of the polynomial

$\, 4x^5 + x^3 + 2x^2$

is 4.

The coefficients of polynomial also may be in the other order:

$Q(x) = a_0 x^k + a_1 x^{k-1} + \cdots + a_{k-1} x^1 + a_k$

and must be a₀≠0 and a₀ is the leading coefficient of Q.

Important coefficients in mathematics include the binomial coefficients which are coefficients in the statement of the binomial theorem. These can be partially found with Pascal's triangle.

1 Linear algebra
2 Examples of physical coefficients
3 Chemistry
4 See also

Linear algebra

For In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given

$M = \begin{bmatrix}1 & 2 & 0 & 6 \\ 0 & 2 & 9 & 4 \\ 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 \end{bmatrix}.$

The leading coefficient of the first row is 1, 2 is the leading coefficient of the second row, 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.

Examples of physical coefficients

Coefficient of Thermal Expansion (thermodynamics) (dimensionless) - Relates the change in temperature to the change in a material's dimensions.
Partition Coefficient (K_D) (chemistry) - The ratio of concentrations of a compound in two phases of a mixture of two immiscible solvents at equilibrium.
Hall coefficient (electrical physics) - Relates a magnetic field applied to an element to the voltage created, the amount of current and the element thickness. It is a characteristic of the material from which the conductor is made.
airfoil, and the planform area of the airfoil.
Ballistic coefficient (BC) (Aerodynamics) (units of kg/m²) - A measure of a body's ability to overcome air resistance in flight. BC is a function of mass, diameter, and drag coefficient.
Transmission Coefficient (quantum mechanics) (dimensionless) - Represents the probability flux of a transmitted wave relative to that of an incident wave. It is often used to describe the probability of a particle tunnelling through a barrier.
Damping Factor a.k.a. viscous damping coefficient (Physical Engineering) (units of newton-seconds per meter) - relates a damping force with the velocity of the object whose motion is being

Chemistry

A coefficient is a number placed in front of a term in a chemical equation to indicate how many particles take part in the reaction. For example, in the formula $2H_2 + O_2 \rarr 2H_2O$ , the number 2 in front of $H 2$ is a coefficient.

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	association coefficient
	factor (computer jargon)
	index of X (computer jargon)

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coefficient

Contents

Linear algebra

Examples of physical coefficients

Chemistry

See also