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Difference between revisions of "Coefficient"

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A numerical factor in an algebraic expression, a known factor in front of a power of an unknown or a constant factor multiplying a variable quantity. Thus, the coefficient in the monomial <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229001.png" /> is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229002.png" />; in the equation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229003.png" />, the coefficient of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229004.png" /> is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229005.png" />, while that of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229006.png" /> is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229007.png" />; in the formula for the length of a circumference <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229008.png" />, the coefficient is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c0229009.png" />. In the equation of a straight line <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c02290010.png" />, the number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c02290011.png" />, which represents the tangent of the angle at which the straight line is inclined to the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022900/c02290012.png" />-axis, is called the angular coefficient.
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A numerical factor in an algebraic expression, a known factor in front of a power of an unknown or a constant factor multiplying a variable quantity. Thus, the coefficient in the monomial $-(3/4)a^2b^2$ is $-3/4$; in the equation $x^2+2px+q=0$, the coefficient of $x^2$ is $1$, while that of $x$ is $2p$; in the formula for the length of a circumference $l=2\pi r$, the coefficient is $2\pi$. In the equation of a straight line $y=kx+b$, the number $k$, which represents the tangent of the angle at which the straight line is inclined to the $x$-axis, is called the angular coefficient.

Latest revision as of 16:38, 11 April 2014

A numerical factor in an algebraic expression, a known factor in front of a power of an unknown or a constant factor multiplying a variable quantity. Thus, the coefficient in the monomial $-(3/4)a^2b^2$ is $-3/4$; in the equation $x^2+2px+q=0$, the coefficient of $x^2$ is $1$, while that of $x$ is $2p$; in the formula for the length of a circumference $l=2\pi r$, the coefficient is $2\pi$. In the equation of a straight line $y=kx+b$, the number $k$, which represents the tangent of the angle at which the straight line is inclined to the $x$-axis, is called the angular coefficient.

How to Cite This Entry:
Coefficient. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Coefficient&oldid=14391
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article