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Determinant: meaning, definitions and examples

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determinant

 

[ dษชหˆtษœหrmษชnษ™nt ]

Noun
Context #1 | Noun

mathematics

In mathematics, a determinant is a scalar value that can be computed from the elements of a square matrix. It encapsulates key information about the matrix, including whether the matrix is invertible and the volume scaling factor of the linear transformation described by the matrix. The determinant is denoted as det(A) for a matrix A and can be calculated using various methods, including cofactor expansion or row reduction. Determinants are particularly significant in solving systems of linear equations and in linear algebra applications.

Synonyms

determinative, factor.

Examples of usage

  • To determine if the matrix is invertible, calculate its determinant.
  • The area of the parallelogram can be found using the determinant of vectors.
  • The determinant of the identity matrix is always one.

Translations

Translations of the word "determinant" in other languages:

๐Ÿ‡ต๐Ÿ‡น determinante

๐Ÿ‡ฎ๐Ÿ‡ณ เคจเคฟเคฐเฅเคงเคพเคฐเค•

๐Ÿ‡ฉ๐Ÿ‡ช Determinante

๐Ÿ‡ฎ๐Ÿ‡ฉ penentu

๐Ÿ‡บ๐Ÿ‡ฆ ะดะตั‚ะตั€ะผั–ะฝะฐะฝั‚

๐Ÿ‡ต๐Ÿ‡ฑ wyznacznik

๐Ÿ‡ฏ๐Ÿ‡ต ่กŒๅˆ—ๅผ

๐Ÿ‡ซ๐Ÿ‡ท dรฉterminant

๐Ÿ‡ช๐Ÿ‡ธ determinante

๐Ÿ‡น๐Ÿ‡ท belirleyici

๐Ÿ‡ฐ๐Ÿ‡ท ํ–‰๋ ฌ์‹

๐Ÿ‡ธ๐Ÿ‡ฆ ุงู„ู…ุญุฏุฏ

๐Ÿ‡จ๐Ÿ‡ฟ determinant

๐Ÿ‡ธ๐Ÿ‡ฐ determinant

๐Ÿ‡จ๐Ÿ‡ณ ่กŒๅˆ—ๅผ

๐Ÿ‡ธ๐Ÿ‡ฎ determinanta

๐Ÿ‡ฎ๐Ÿ‡ธ รกkvarรฐandi

๐Ÿ‡ฐ๐Ÿ‡ฟ ะฐะฝั‹า›ั‚ะฐา“ั‹ัˆ

๐Ÿ‡ฌ๐Ÿ‡ช แƒ“แƒแƒ“แƒ’แƒ”แƒœแƒ˜แƒšแƒ˜

๐Ÿ‡ฆ๐Ÿ‡ฟ tษ™yin edici

๐Ÿ‡ฒ๐Ÿ‡ฝ determinante

Etymology

The word 'determinant' first appeared in English in the 19th century, deriving from the Latin root 'determinare', meaning 'to limit' or 'to define'. Its mathematical usage has roots in linear algebra, where the concept was developed to provide a way to understand the properties of square matrices. The term reflects its function in mathematics as a defining factor or a limit to the properties of linear transformations. Over time, 'determinant' has become a standard term in mathematics, particularly in discussions involving matrices and linear equations, emphasizing its fundamental role in the field.

Word Frequency Rank

Ranked #10,905, this word falls into high-advanced vocabulary. It appears less frequently but is valuable for expressing precise meanings in specific contexts.