sign

Sign of real or complex value

Syntax

sign(z)

Description

sign(z) returns the sign of real or complex value z. The sign of a complex number z is defined as z/abs(z). If z is a vector or a matrix, sign(z) returns the sign of each element of z.

Examples

Signs of Real Numbers

Find the signs of these symbolic real numbers:

[sign(sym(1/2)), sign(sym(0)), sign(sym(pi) - 4)]

ans =
[ 1, 0, -1]

Signs of Matrix Elements

Find the signs of the real and complex elements of matrix A:

A = sym([(1/2 + i), -25; i*(i + 1), pi/6 - i*pi/2]);
sign(A)

ans =
[   5^(1/2)*(1/5 + 2i/5),                              -1]
[ 2^(1/2)*(- 1/2 + 1i/2), 5^(1/2)*18^(1/2)*(1/30 - 1i/10)]

Sign of Symbolic Expression

Find the sign of this expression assuming that the value x is negative:

syms x
assume(x < 0)
sign(5*x^3)

ans =
-1

For further computations, clear the assumption on x by recreating it using syms:

syms x

Input Arguments

z — Input

symbolic number | symbolic variable | symbolic expression | symbolic function | symbolic vector | symbolic matrix

Input specified as a symbolic number, variable, expression, function, vector, or matrix.

More About

Sign Function

The sign function of any number z is defined via the absolute value of z:

$$\mathrm{sign}\left(z\right)=\frac{z}{\left|z\right|}$$

Thus, the sign function of a real number z can be defined as follows:

$$\mathrm{sign}\left(z\right)=\{\begin{array}{c}-1\text{ if }x<0\\ 0\text{ if }x=0\\ 1\text{ if }x>0\end{array}$$

Tips

• Calling sign for a number that is not a symbolic object invokes the MATLAB^® sign function.