Signum function

In mathematics 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:

Any real number can be expressed as the product of its absolute value and its sign function:

From equation (1) it follows that

but equation (2) is indeterminate when x is set to zero.

The signum function is the derivative of the absolute value function (up to the indeterminacy at zero):

Also, the derivative of the signum function is two times the Dirac delta function,

The signum function is related to the Heaviside step function h_0.5(x) thus

sgnx = 2h_0.5(x) - 1,

where the 0.5 subscript of the step function means that h_0.5(0) = 0.5.

Also, if the step function h₀(x) is thought of as a mathematical switch, with h₀(x) = 0, then the signum function can be expressed as

See also

• Negative and non-negative numbers