# 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.

## 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.
References in periodicals archive ?
Mangasarian, "Absolute value equation solution via concave minimization," Optimization Letters, vol.1, no.1, pp.3-8, 2007.
To find the equations of the line segments that make up the graphs, one can "go algebraic" and fall back on the algebraic definition of absolute value:
However, to avoid ambiguity with analytical expression of their absolute values as well as with sorting of their values, we have to restrict the derivation only for their positive values.
The absolute value of a, denoted by [absolute value of a], will be defined by
They are of absolute value because they are grounded on the dignity of each human life and person.
"The challenge is to live an honourable life in a world that no longer has absolute values," he says.

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