# Dictionary Definition

coefficient n : a constant number that serves as
a measure of some property or characteristic

# User Contributed Dictionary

## English

### Pronunciation

- a UK /ˌkəʊˈɪ.fɪʃn̩t/|/ˌkəʊˈi.fɪʃn̩t/, 1=/%k@U"I.fISn=t/|2=/%k@U"i.fISn=t/

cooperating

- Dutch: behulpzaam
- Finnish: myötävaikuttava
- Spanish: coeficiente

### Noun

- A constant by which an algebraic term is multiplied.
- A number, value or item that serves as a measure of some property or characteristic.

#### Translations

algebraic constant

- Czech: koeficient, součinitel
- Dutch: coëfficiënt
- Finnish: kerroin
- French: coefficient
- German: Koeffizient
- Hungarian: együttható
- Italian: coefficiente
- Spanish: coeficiente

measure of some property or characteristic

- Dutch: coëfficiënt
- Finnish: kerroin
- German: Koeffizient

- ttbc French: coefficient
- ttbc Hungarian: együttható
- ttbc Italian: coefficiente
- ttbc Spanish: coeficiente

## French

### Pronunciation

- /kɔ.e.fi.sjɑ̃/|lang=fr, /kO.e.fi.sjA~/|lang=fr

### Noun

fr-noun m# Extensive Definition

In mathematics, a coefficient
is a constant multiplicative factor of
a certain 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

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

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

- \, 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^ + \cdots + a_ 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.

## Linear algebra

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 = \begin1 & 2 & 0 & 6 \\

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 (KD) (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.
- Lift Coefficient (CL or CZ) (Aerodynamics) (dimensionless) - Relates the lift generated by an airfoil with the dynamic pressure of the fluid flow around the 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 dampened.

## See also

coefficient in Bulgarian: Коефициент

coefficient in Catalan: Coeficient

coefficient in Czech: Koeficient

coefficient in German: Koeffizient

coefficient in Esperanto: Koeficiento

coefficient in French: Coefficient

coefficient in Korean: 계수

coefficient in Ido: Koeficiento

coefficient in Icelandic: Stuðull
(stærðfræði)

coefficient in Dutch: Coëfficiënt

coefficient in Japanese: 係数

coefficient in Norwegian: Koeffisient

coefficient in Russian: Коэффициент

coefficient in Simple English: Coefficient

coefficient in Slovak: Matematický
koeficient

coefficient in Slovenian: Koeficient

coefficient in Finnish: Kerroin

coefficient in Swedish: Koefficient

coefficient in Urdu: عددی سر

coefficient in Chinese: 系数

# Synonyms, Antonyms and Related Words

coacting, coactive, coadjutant, coadjuvant, collaborative, collective, collectivist, collectivistic, collusive, combined, commensal, common, communal, communalist, communalistic, communist, communistic, communitarian, concerted, concordant, concurrent, concurring, conjoint, conniving, cooperant, cooperating, cooperative, ecumenic, fellow, harmonious, harmonized, joint, mutual, noncompetitive, reciprocal, symbiotic, synergetic, synergic, synergistic, uncompetitive