# absolute value

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## absolute value,

magnitude of a number or other mathematical expression disregarding its sign; thus, the absolute value is positive, whether the original expression is positive or negative. In symbols, if |*a*| denotes the absolute value of a number

*a,*then |

*a*| =

*a*for

*a*> 0 and |

*a*| = −

*a*for

*a*< 0. For example, |7|= 7 since 7 > 0 and |−7| = −(−7), or |−7| = 7, since −7 < 0.

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## absolute value

[′ab·sə‚lüt ′val·yü]Also known as magnitude.

(mathematics)

For a real number, the number if it is nonnegative, and the negative of the number if it is negative. Also known as numerical value.

For a complex number, the square root of the sum of the squares of its real and imaginary parts. Also known as modulus.

The length of a vector, disregarding its direction; the square root of the sum of the squares of its orthogonal components.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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