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In mathematics, a coefficient is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient of 9x2 is 9. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as
where an is the coefficient of the variable xn for each n = 1, 2, 3, …
In a polynomial P(x) of one variable x, the coefficient of xk can be indexed by k, giving the convention that for example
For the largest k where ak ≠ 0, ak is called the leading coefficient of P because most often, polynomials are written from the largest power of x, downward (i.e. x5 + x4 + x2 ...).
In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given
1 is the leading coefficient of the first row, 2 is the leading coefficient of the second row, 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.
In physics, many equations have coefficients associated with them. For example, is the coefficient of friction between two objects in the equation .
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