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Signum Function

The signum function is the real valued function defined for real typeset structure as follows

sgn(x) = {+ 1,         if x > 0,            0,           if x = 0,            -1,          if x < 0.


For all real typeset structure we have  typeset structure. Similarly,  typeset structure. If typeset structure then also typeset structure. The second property implies that for real non-zero typeset structure we have typeset structure.  

For a complex argument typeset structure it is defined by

sgn(z) = {            0,         if z = 0,              z           -----,           | z |      if z != 0,

where typeset structure denotes the magnitude (absolute value) of typeset structure. In other words, the signum function project a non-zero complex number to the unit circle typeset structure.

We have typeset structure, where typeset structure is the complex conjugate of typeset structure.

Cite this web-page as:

Štefan Porubský: Signum Function.

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