# determinant

## English

English Wikipedia has an article on:
Wikipedia

### Etymology

Borrowed from French déterminant.

### 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 ${\displaystyle A_{(n)}}$  is a function (actually a polynomial function) of the elements ${\displaystyle a_{ij}}$  of ${\displaystyle A}$ .
• 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.
4. (genetics) Something that causes a nuclease to cut at a specified point

#### Derived terms

determinant (comparative more determinant, superlative most determinant)

1. Serving to determine or limit; determinative.

### References

1. ^ determinant”, in Merriam–Webster Online Dictionary.

## Catalan

### Verb

determinant

1. present participle of determinar

## Czech

### Noun

determinant m

1. determinant (unique scalar function over square matrices)

### Related terms

• determinant in Příruční slovník jazyka českého, 1935–1957
• determinant in Slovník spisovného jazyka českého, 1960–1971, 1989

## Danish

### Noun

determinant c (singular definite determinanten, plural indefinite determinanter)

1. (linear algebra) determinant

dēterminant

## Norwegian Bokmål

Norwegian Wikipedia has an article on:
Wikipedia no

### 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.

## Norwegian Nynorsk

Norwegian Nynorsk Wikipedia has an article on:
Wikipedia nn

### 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)

## Slovak

### Noun

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

1. determining factor
2. (mathematics) determinant

## 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