Coefficient

views updated May 29 2018

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 means3 times x), and 2 (because 2y means 2 times y). Therefore, the coefficient of xy is 5, the coefficient of x is3, 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.

coefficient

views updated May 21 2018

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 4xy).2. Physics a multiplier or factor that measures some property: coefficients of elasticity the drag coefficient.

Coefficient

views updated May 23 2018

Coefficient

A coefficient 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:

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 2 - 3x + 2y - 4-X are considered to be 5, -3, +2, and -4.

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

coefficient

views updated May 29 2018

coefficient Term multiplying a specified unknown quantity in an algebraic expression. In the expression 1 + 5x + 2x2, 5 and 2 are the coefficients of x and x2 respectively. In physics, it is a ratio that yields a pure number or a quantity with dimensions.

coefficient

views updated Jun 27 2018

coefficient XVII. — modL. coefficiens; see CO- and EFFICIENT.

coefficient

views updated May 18 2018

coefficient See ASSOCIATION COEFFICIENTS.