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 coefficients which are coefficients in the statement of the binomial theorem. These can be partially found with Pascal's triangle.

Contents

Linear algebra

Physics

See also

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
:
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

★ degree of a polynomial

★ monic polynomial