absolute value

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absolute value

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absolute value (plural absolute values)

1. (mathematics) For a complex number ${\displaystyle a+bi}$, the principal square root of the sum of the squares of its real and imaginary parts, ${\displaystyle {\sqrt {a^{2}+b^{2}}}}$. Denoted by vertical bars ${\displaystyle |\,|}$.

   The absolute value ${\displaystyle |x|}$ of a real number ${\displaystyle x}$ is ${\displaystyle {\sqrt {x^{2}}}}$, which is equal to ${\displaystyle x}$ if ${\displaystyle x}$ is non-negative, and ${\displaystyle -x}$ if ${\displaystyle x}$ is negative.

• modulus

• Euclidean norm
  • norm

• p-adic absolute value
• trivial absolute value