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In mathematics, a **coefficient** is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient of *9x*^{2} is *9*. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as

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

For the largest *k* where *a*_{k} ≠ 0, *a*_{k} is called the * leading coefficient* of

*P*because most often, polynomials are written from the largest power of

*x*, downward (i.e.

*x*

^{5}+

*x*

^{4}+

*x*

^{2}...).

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

1 is the leading coefficient of the first row, 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.

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

In physics, many equations have coefficients associated with them. For example, is the coefficient of friction between two objects in the equation .

## See also[]

- degree of a polynomial
- monic polynomial

- bg:Коефициент

cs:Koeficient de:Koeffizient es:Coeficiente fr:Coefficient io:Koeficiento nl:Coëfficiënt no:Koeffisient ru:Коэффициент sv:Koefficient

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