coefficient

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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.

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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.

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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 .

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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.

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

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coefficient See ASSOCIATION COEFFICIENTS.