# determinant
## English
### Etymology

Borrowed from French déterminant.

### Pronunciation

* (UK, General Australian) IPA: /dɪˈtɜːmɪnənt/
* (General American, Canada) IPA: /dɪˈtɝmɪnənt/, /dɪˈtɝmənənt/
* Audio (US):(file)

### Noun

determinant (plural determinants)
* 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”, in Richard Wilkinson, Michael Marmot, editors, Social Determinants of Health: The Solid Facts, 2nd edition, World Health Organization, 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.
* (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.
* (biology) A substance that causes a cell to adopt a particular fate.
* (genetics) Something that causes a nuclease to cut at a specified point

#### Derived terms

* allodeterminant
* antideterminant
* bideterminant
* cytoplasmic determinant
* determinantal
* hyperdeterminant
* immunodeterminant
* macrodeterminant, microdeterminant
* multideterminant
* predeterminant
* quasideterminant
* serodeterminant
* Slater determinant
* stereodeterminant
* subdeterminant
* superdeterminant

#### Translations
### Adjective

determinant (comparative more determinant, superlative most determinant)
* Serving to determine or limit; determinative.

#### Derived terms

* self-determinant

### See also

* permanent
* singular

### References

* ↑ “determinant”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.

### Further reading

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

### Anagrams

* detrainment

## Catalan
### Adjective

determinant m or f (masculine and feminine plural determinants)
* determining
    factor determinant ― determining factor

### Noun

determinant m (plural determinants)
* (grammar) determiner
* (mathematics) determinant

### Verb

determinant
* gerund of determinar

## Czech
### Pronunciation

* IPA: [ˈdɛtɛrmɪnant]

### Noun

determinant m inan
* determinant (unique scalar function over square matrices)

#### Related terms

* See termín

### Further reading

* “determinant”, in Příruční slovník jazyka českého (in Czech), 1935–1957
* “determinant”, in Slovník spisovného jazyka českého (in Czech), 1960–1971, 1989

## Danish
### Noun

determinant c (singular definite determinanten, plural indefinite determinanter)
* (linear algebra) determinant

#### Declension
### Further reading

* “determinant” in Den Danske Ordbog

## Latin
### Verb

dēterminant
* 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)
* determinant (determining factor)
* (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)
* determinant (determining factor)
* (linear algebra) determinant (mathematical term)

### References

* “determinant” in The Nynorsk Dictionary.

## Romanian
### Etymology

Borrowed from French déterminant.

### Adjective

determinant m or n (feminine singular determinantă, masculine plural determinanți, feminine and neuter plural determinante)
* determinant

#### Declension
## Slovak
### Pronunciation

* IPA: [ˈdeterminant]

### Noun

determinant m inan
* determining factor
* (mathematics) determinant

#### Declension
### 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, 2003–2025

## Swedish
### Noun

determinant c
* (mathematics) determinant

#### Declension

| | | nominative | genitive |
| singular | indefinite | determinant | determinants |
| singular | definite | determinanten | determinantens |
| plural | indefinite | determinanter | determinanters |
| plural | definite | determinanterna | determinanternas |