determinant

See also: déterminant

English

Etymology

Borrowed from French déterminant.

Pronunciation

• IPA^(key): /dɪˈtɜːmɪnənt/
• IPA^(key): /dɪˈtʌɹmɪnənt/

Noun

determinant (plural determinants)

1. A determining factor; an element that determines the nature of something.
   • 1999, Noah P. Barsky, Stuart Bruchey (editor), Organizational Determinants of Budgetary Influence and Involvement, Taylor & Francis (Garland Publishing), page 4,

     Shields and Young (1993) argue that the budget participation literature "has not produced a coherent nor unified definition" of both the determinants and consequences of budget participation.

   • 2003, Agis D. Tsouros, Foreword, Richard Wilkinson, Michael Marmot (editors), Social Determinants of Health: The Solid Facts, World Health Organization, 2nd Edition, page 5,

     The field of the social determinants of health is perhaps the most complex and challenging of all.

   • 2004, Carsten Anckar, Determinants of the Death Penalty: A comparative study of the world, Taylor & Francis (Routledge), page 165,

     The aim of this book has been to assess the determinants of capital punishment without taking a stand for or against the death penalty.

2. (linear algebra) A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det.
   • 1966 [Allyn & Bacon], Howard Whitley Eves, Elementary Matrix Theory, 1980, Dover, Unabridged corrected republication, page 165,

     The determinant of a square matrix $A_{(n)}$ is a function (actually a polynomial function) of the elements $a_{ij}$ of $A$.

   • 1990, Assem S. Deif, Advanced Matrix Theory for Scientists and Engineers, Gordon and Breach Science Publishers (Abacus Press), 2nd Edition, page 18,

     Show that the determinant of a Hermitian matrix is real and that of a skew-Hermitian matrix is imaginary.

   • 2009, Richard A. Brualdi, Dragoš Cvetkoviċ, A Combinatorial Approach to Matrix Theory and Its Applications, Taylor & Francis (CRC / Chapman & Hall), page 63,

     Using this definition, we derive the basic properties of a determinant that are useful in its evaluation. In particular, it is shown how the calculation of a determinant can be reduced to the calculation of determinants of lower order.

3. (biology) A substance that causes a cell to adopt a particular fate.

Translations

determining factor

• Chinese:

  Mandarin: 決定(性)因素／决定(性)因素, 决定(性)因素 (juédìng(xìng) yīnsù)

• Finnish: määräävä tekijä, ratkaiseva tekijä
• French: déterminant (fr) m
• Hungarian: meghatározó (hu)
• (deprecated template usage) {{trans-mid}}
• Irish: cinntitheach m
• Norwegian: determinant m
• Portuguese: determinante (pt) m
• Russian: определя́ющий фа́ктор m (opredeljájuščij fáktor), определи́тель (ru) m (opredelítelʹ)

scalar that encodes certain characteristics of a square matrix

• Bulgarian: детерминанта f (determinanta)
• Chinese:

  Mandarin: 行列式 (zh) (hánglièshì)

• Czech: determinant (cs) m
• Danish: determinant c
• Estonian: determinant
• Finnish: determinantti (fi)
• French: déterminant (fr) m
• German: Determinante (de) f
• Greek: ορίζουσα (el) f (orízousa)
• Hungarian: determináns (hu)
• (deprecated template usage) {{trans-mid}}
• Icelandic: ákveða f
• Italian: determinante (it) m
• Japanese: 行列式 (ja) (gyōretsu-shiki)
• Norwegian: determinant m
• Polish: wyznacznik (pl) m
• Portuguese: determinante (pt) m
• Russian: детермина́нт (ru) m (determinánt)
• Slovak: determinant m
• Spanish: determinante (es) m
• Swedish: determinant (sv) c
• Tagalog: taliyak

Derived terms

• determinantal
• macrodeterminant, microdeterminant

Adjective

determinant (comparative more determinant, superlative most determinant)

1. Serving to determine or limit; determinative.

See also

• permanent
• singular

Further reading

• Risk factor on Wikipedia.Wikipedia
• Determinantal variety on Wikipedia.Wikipedia
• Determinant on Wolfram MathWorld
• Determinant on Encyclopedia of Mathematics

Anagrams

• detrainment

---

Catalan

Verb

determinant

---

Czech

Pronunciation

• IPA^(key): [ˈdɛtɛrmɪnant]

Noun

1. determinant (unique scalar function over square matrices)

Related terms

• See termín

Further reading

• Template:R:PSJC
• Template:R:SSJC

---

Danish

Noun

determinant c (singular definite determinanten, plural indefinite determinanter)

1. (linear algebra) determinant

Declension

Declension of determinant

common gender	Singular		Plural
	indefinite	definite	indefinite	definite
nominative	determinant	determinanten	determinanter	determinanterne
genitive	determinants	determinantens	determinanters	determinanternes

Further reading

• “determinant” in Den Danske Ordbog

---

Latin

Verb

(deprecated template usage) dēterminant

1. third-person plural present active indicative of dēterminō

---

Norwegian Bokmål

Etymology

From Latin determinant, from determinare

Noun

determinant m (definite singular determinanten, indefinite plural determinanter, definite plural determinantene)

1. determinant (determining factor)
2. (linear algebra) determinant (mathematical term)

   Determinanten til identitetsmatrisa er 1.

   The determinant of the identity matrix equals 1.

References

• “determinant” in The Bokmål Dictionary.

---

Norwegian Nynorsk

Etymology

From Latin determinant, from determinare

Noun

determinant m (definite singular determinanten, indefinite plural determinantar, definite plural determinantane)

1. determinant (determining factor)
2. (linear algebra) determinant (mathematical term)

References

• “determinant” in The Nynorsk Dictionary.

---

Slovak

Pronunciation

• IPA^(key): /ˈdɛtɛrminant/

Noun

determinant m (genitive singular determinantu, nominative plural determinanty, genitive plural determinantov, declension pattern of dub)

1. determining factor
2. (mathematics) determinant

Declension

Declension of determinant

	singular	plural
nominative	determinant	determinanty
genitive	determinantu	determinantov
dative	determinantu	determinantom
accusative	determinant	determinanty
locative	determinantoch	determinantoch
instrumental	determinantom	determinantmi

Further reading

• “determinant”, in Slovníkový portál Jazykovedného ústavu Ľ. Štúra SAV [Dictionary portal of the Ľ. Štúr Institute of Linguistics, Slovak Academy of Science] (in Slovak), https://slovnik.juls.savba.sk, 2024

---

Swedish

Noun

determinant c

1. (mathematics) determinant

Declension

Declension of determinant
	Singular		Plural
	Indefinite	Definite	Indefinite	Definite
Nominative	determinant	determinanten	determinanter	determinanterna
Genitive	determinants	determinantens	determinanters	determinanternas