Sign function

The sign function or signum function (from the Latin signum sign ) is in mathematics a function that assigns a real or complex number sign.

• 2.1 Definition
• 2.2 Calculation Rules

Sign function on the real numbers

Definition

The real sign of function forms the set of real numbers into the set off and is usually defined as follows:

So It assigns to the positive numbers the value 1, the negative numbers -1 and 0 the value 0.

For applications in the computing technology is dispensed mostly on a special position of 0, by matching the positive, negative or two speed ranges. This allows the sign of a number in a single bit encoding. The sign function is beyond the weak derivative of the absolute value function.

Derivative and integral

The sign function is neither differentiable classic, yet it has a weak derivative. However, it is differentiable in terms of distributions, and its derivative, wherein the delta function called.

But applies to all.

Moreover, for all

Sign function on the complex numbers

Definition

Compared to the sign function of real numbers, the following expansion is rarely considered to complex numbers:

The result of this function is for on the unit circle and has the same argument as the output value, in particular applies

Example: (red in the picture)

Calculation rules

For the complex sign function, the following calculation rules apply:

For all complex numbers, and the following applies:

• For all with the amount of designated;
• Wherein the cross bar denotes complex conjugation;
• , in particular   for positive real,
• For negative real,
• ;