abs

Computes absolute values.

Syntax

• abs(x)

  • x is a number, vector, or matrix

Description

If x is a real or complex number, abs(x) is the absolute value of x.

• For real x, abs(x) is x if x ≥ 0 and −x otherwise. If x is of type integer or rational number, so is abs(x).

• For complex z = a + b⋅i (with a and b real), abs(z) is √(a² + b²). The type of abs(z) is real number.

If x is a vector or a matrix, abs(x) is the vector or matrix obtained by taking element-wise absolute values. abs(x) is always a real vector or matrix, even if x is a complex vector or matrix.

Examples

abs(10)

10

abs(−10)

10

abs(3 + 4⋅i)

5

abs(❨1, −1, 0❩)

 ⎛1⎞
e⎜1⎟
 ⎝0⎠

abs(❨❨1, i❩, ❨−i, −2❩❩)

⎛1 1⎞
⎝1 2⎠

See also

• arg

• norm