In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c). When the coefficients are themselves variables, they may also be called parameters.
The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter c, respectively. The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and a, respectively.
In many scenarios, coefficients are numbers (as is the case for each term of the previous example), although they could be parameters of the problem—or any expression in these parameters. In such a case, one must clearly distinguish between symbols representing variables and symbols representing parameters. Following René Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but this is not always the case. For example, if y is considered a parameter in the above expression, then the coefficient of x would be −3y, and the constant coefficient (with respect to x) would be 1.5 + y.
The leading entry (sometimes leading coefficient) of a row in a matrix is the first nonzero entry in that row. So, for example, in the matrix