Coefficient

A coefficient, in mathematics, is a constant multiplier of variables and any part of an algebraic term. Thus, in the expression:

the possible coefficients for the term 3xy² would include 3, which is the coefficient of xy², and x, which is the coefficient of 3y²:

and has 4 as a coefficient of

Most commonly, however, the word coefficient refers to what is, strictly speaking, the numerical coefficient. Thus, the numerical coefficients of the expression 5xy - 3x+ 2y are considered to be 5 (because 5xy means 5 times x times y), –3 (because -3x means–3 times x), and 2 (because 2y means 2 times y). Therefore, the coefficient of xy is 5, the coefficient of x is–3, and the coefficient of y is 2. The x and y variables are not considered coefficients in this case because they are variables, not numbers. In general algebraic expressions, such as ax+ by², the letters a and b are coefficients for x and y², respectively, because they are representing possible numbers.

In a polynomial such as Q(y) = 4y³+ 2y+ 5, the coefficient 4 associated with the largest power of y, in this case 4y³, is called the leading coefficient of Q. The other coefficients are 2 and 5.

The leading coefficient in a matrix, within linear algebra, is the first nonzero entry in a row. If the matrix M = [0 8 9 3 7], then 8 is the leading coefficient for that row.

In many formulas, especially in statistics, certain numbers are considered coefficients, such as correlation coefficients in statistics or the coefficient of expansion in physics.

co·ef·fi·cient / ˌkōəˈfishənt/ • n. 1. Math. a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x^y).2. Physics a multiplier or factor that measures some property: coefficients of elasticity the drag coefficient.