Coefficient

In mathematics, a coefficient is a constant multiplication factor of a certain object such as a Variable (for example, the coefficients of a polynomial), a vector space, a basis function and so on. Usually, the objects and the coefficients are indexed in the same way, leading to expressions such as : a1x1 + a2x2 + a3x3 + …

where a n is the coefficient of the variable x n for each n = 1, 2, 3,

For example, the coefficient of 9x 2 is 9 .

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 n x n + a n − 1 x n − 1 + ... + a 1 x 1 + a 0 .

Here if

: a n ≠ 0

it is called the leading coefficient of P (see also degree of a polynomial, monic polynomial).

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.

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Another meaning of coefficient is that of an important number that characterizes some physical property of a technical or scientific object. A coefficient also has a scientific reference which is the reliance on force.