See Also

Sign function

In mathematics Mathematics

Mathematics is the discipline that deals with concepts such as quantity [i], structure [i], space [i] a ... 

 and especially in computer science, the sign function is a logical function which extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function. The sign function is often represented as sgn and can be defined thus: or using the Iverson bracket notation: Any real number can be expressed as the product of its absolute value Absolute value

In mathematics [i], the absolute value of a real number [i] is its numerical value without regard to it ... 

 and its sign function: From equation it follows that whenever x is not equal to 0 we have The signum function is the derivative Derivative

In mathematics [i], the derivative is defined as the instantaneous rate of change of a function [i] ... 

 of the absolute value function :

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Encyclopedia



In mathematics Mathematics

Mathematics is the discipline that deals with concepts such as quantity [i], structure [i], space [i] a ... 

 and especially in computer science, the sign function is a logical function which extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function. The sign function is often represented as sgn and can be defined thus:

or using the Iverson bracket notation:

Any real number can be expressed as the product of its absolute value Absolute value

In mathematics [i], the absolute value of a real number [i] is its numerical value without regard to it ... 

 and its sign function:
From equation it follows that whenever x is not equal to 0 we have

The signum function is the derivative Derivative

In mathematics [i], the derivative is defined as the instantaneous rate of change of a function [i] ... 

 of the absolute value function :

The signum function is differentiable with derivative 0 everywhere except at 0. It is not differentiable at 0 in the ordinary sense, but under a somewhat generalised notion of differentiation , we can say that the derivative of the signum function is two times the Dirac delta function Dirac delta function

The Dirac delta or Dirac's delta, often referred to as the unit impulse function and introduced by... 

,

The signum function is related to the Heaviside step function Heaviside step function

The Heaviside step function, sometimes called the unit step function [i] and named in honor of Oliver Heaviside [i] ... 

 H1/2 thus
where the 1/2 subscript of the step function means that H1/2 = 1/2

Complex Signum


The signum function can be generalized to complex numbers Complex number

In mathematics [i], a complex number is a number [i] of the form
... 

 as

for any z ? except z=0. The signum of a given complex number, z is the point on the unit circle Unit circle

In mathematics [i], a unit circle is a circle [i] with unit [i] radius [i], i.e., a circle whose radiu ... 

 of the complex plane Complex plane

In mathematics [i], the complex plane is a geometric space of the complex numbers [i] as set up by the ' ... 

 that is nearest to z.

Because zero has an equal distance to all points on the unit circle, it is generally given the signum 0.

See also

  • Negative and non-negative numbers
  • Absolute value Absolute value

    In mathematics [i], the absolute value of a real number [i] is its numerical value without regard to it ...