absolute value

English

Alternative forms

• | | (vertical bars)

Pronunciation

• (US) IPA^(key): /ˈæb.səˌlut ˈvæl.ju/, /ˌæb.səˈljut ˈvæl.ju/

• Audio (Southern England):

  (file)

Noun

absolute value (plural absolute values)

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

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

Synonyms

• modulus

Hypernyms

• Euclidean norm
  • norm

Derived terms

• p-adic absolute value
• trivial absolute value

Translations

numerical value of a real number

• Arabic: قِيمَة مُطْلَقَة f (qīma muṭlaqa)
• Armenian: բացարձակ արժեք (bacʻarjak aržekʻ)
• Asturian: valor absolutu m
• Catalan: valor absolut m
• Chinese:

  Mandarin: 絕對值 / 绝对值 (zh) (juéduìzhí)

• Czech: absolutní hodnota f
• Danish: numerisk værdi c
• Dutch: absolute waarde (nl) f
• Esperanto: absoluta valoro
• Finnish: itseisarvo (fi)
• French: valeur absolue (fr) f
• Galician: valor absoluto m
• German: Absolutwert f, Betrag (de) f
• Hungarian: abszolút érték (hu)
• Italian: valore assoluto (it) m
• Japanese: 絶対値 (ja) (ぜったいち, zettaichi)
• Korean: 절대값 (ko) (jeoldaegap)
• Malay: nilai mutlak (ms)
• Polish: wartość bezwzględna f
• Portuguese: valor absoluto m
• Romanian: valoare absolută (ro) f
• Russian: абсолю́тная величина́ f (absoljútnaja veličiná)
• Slovak: absolútna hodnota (sk) f
• Slovene: absolutna vrednost f
• Spanish: valor absoluto m
• Swedish: absolutbelopp (sv) n, belopp (sv) n
• Tagalog: halgang wagas
• Vietnamese: giá trị tuyệt đối (vi)

modulus of a complex number

• Arabic: قِيمَة مُطْلَقَة f (qīma muṭlaqa)
• Asturian: módulu m, valor absolutu m, magnitú f
• Catalan: mòdul (ca) m, valor absolut m
• Dutch: modulus (nl) m
• Esperanto: absoluta valoro, modulo
• Finnish: itseisarvo (fi), moduli
• French: module (fr), valeur absolue (fr) f
• Galician: módulo (gl) m, valor absoluto m
• German: Absolutwert m
• Hungarian: abszolút érték (hu)
• Italian: modulo (it) m, valore assoluto (it) m
• Japanese: 絶対値 (ja) (ぜったいち, zettaichi)
• Polish: wartość bezwzględna f
• Portuguese: módulo (pt) m
• Russian: абсолю́тная величина́ f (absoljútnaja veličiná), мо́дуль (ru) m (módulʹ)
• Slovak: absolútna hodnota (sk) f, modul m
• Spanish: módulo (es) m, valor absoluto m, magnitud (es) f
• Swedish: absolutbelopp (sv) n, belopp (sv) n, modulus n
• Tagalog: halgang wagas