Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system. This can apply to scalar or vector quantities. The symbol for absolute value is a pair of vertical lines, one on either side of the quantity whose absolute value is to be determined.
Suppose x is a real number. Then the absolute value of x is defined as follows:
For x = 0 or x > 0, | x | = x
For x < 0, | x | = - x
Alternatively, the absolute value of a real number x is equal to the positive square root of x 2 :
| x | = ( x 2 ) 1/2
Let a + jb be a complex number, where a and b are real numbers and j is the positive square root of -1. (The symbol j is standard in engineering practice; mathematicians symbolize the positive square root of -1 as i .) Then the absolute value of a + jb , also called the modulus, is defined as follows:
| a + jb | = ( a 2 + b 2 ) 1/2
The absolute value of a vector in n dimensions is defined in terms of the coordinates of its termination point, in Cartesian n -space, assuming its origin coincides with the point where all coordinate values are zero. Suppose v is a vector in n dimensions, represented by the following coordinates:
v = ( v 1 , v 2 , v 3 , ..., v n )
Then the absolute value of v is given by:
| v | = ( v 1 2 + v 2 2 + v 3 2 + ... + v n 2 ) 1/2
Also see Mathematical Symbols .