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Coefficient




In Mathematics , a coefficient is a Constant Multiplicative factor of a certain object. For example, the coefficient in ''9x''''2'' is ''9''.

The object can be such things as a Variable , a Vector , a Function , etc. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as:
:a_1 x_1 + a_2 x_2 + a_3 x_3 + \cdots
where ''a''''n'' is the coefficient of the variable ''x''''n'' for each ''n'' = 1, 2, 3, …

In a Polynomial ''P''(''x'') of one variable ''x'', the coefficient of ''x''''k'' can be indexed by ''k'', giving the convention that for example:
:P(x) = a_k x^k + \cdots + a_1 x^1 + a_0.
For the largest ''k'' where ''a''''k'' ≠ 0, ''a''''k'' is called the ''leading coefficient'' of ''P'' because most often, polynomials are written from the largest power of ''x'', downward (i.e. ''x''5 + ''x''4 + ''x''2 ...).

Important coefficients in mathematics include the Binomial Coefficient s which are coefficients in the statement of the Binomial Theorem . These can be partially found with Pascal's Triangle .


LINEAR ALGEBRA

In Linear Algebra , the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given

:M = \begin{bmatrix}1 & 2 & 0 & 6 \
0 & 2 & 9 & 4 \
0 & 0 & 0 & 4 \
0 & 0 & 0 & 0
\end{bmatrix}


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.


PHYSICS

In Physics , many equations have coefficients associated with them. For example, \mu is the Coefficient Of Friction between two objects in the equation extbf{F} = \mu extbf{F}_n.


SEE ALSO