the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c, where "c" is a constant, in
when it is understood that these are not considered as variables. Thus a polynomial in one variable x can be written as
for some integer , where are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient. For the largest with (if any), is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial
In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given
The leading coefficient of the first row is 1; 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.
Though coefficients are frequently viewed as constants in elementary algebra, they can be variables more generally. For example, the coordinates of a vector in a vector space with basis , are the coefficients of the basis vectors in the expression
Partition Coefficient (KD) (chemistry) - The ratio of concentrations of a compound in two phases of a mixture of two immiscible solvents at equilibrium. H2O is a coefficient
Hall coefficient (electrical physics) - Relates a magnetic field applied to an element to the voltage created, the amount of current and the element thickness. It is a characteristic of the material from which the conductor is made.
Lift coefficient (CL or CZ) (Aerodynamics) (dimensionless) - Relates the lift generated by an airfoil with the dynamic pressure of the fluid flow around the airfoil, and the plan-form area of the airfoil.
Ballistic coefficient (BC) (Aerodynamics) (units of kg/m2) - A measure of a body's ability to overcome air resistance in flight. BC is a function of mass, diameter, and drag coefficient.