# 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/

#### Translations

cooperating
• Dutch: behulpzaam
• Finnish: myötävaikuttava
• Spanish: coeficiente

### Noun

1. A constant by which an algebraic term is multiplied.
2. 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

## French

### Pronunciation

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

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
where an is the coefficient of the variable xn for each n = 1, 2, 3, …
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.
For the largest k where ak ≠ 0, ak 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^ + \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 \\
0 & 2 & 9 & 4 \\ 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 \end
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

1. Coefficient of Thermal Expansion (thermodynamics) (dimensionless) - Relates the change in temperature to the change in a material's dimensions.
2. Partition Coefficient (KD) (chemistry) - The ratio of concentrations of a compound in two phases of a mixture of two immiscible solvents at equilibrium.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.

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