Determinant Meaning and Definition

Pronunciation

/dɪˈtɛrmɪnənt/ 🔊

Part of Speech

Noun

Definition

A value that results from a mathematical operation, typically denoted by the vertical bar symbol |, which can be used to describe properties of systems, such as linear transformations, determinants, and eigenvalues.

Examples

• The determinant of the matrix was calculated to be 2.
• The theorem states that the determinant of a matrix is equal to the product of its eigenvalues.

Synonyms

• Determiner
• Scalar

Antonyms

• Undetermined
• Indeterminate

Additional Information

A determinant is a fundamental concept in linear algebra, and it is used to describe the properties of matrices and linear transformations. It is often used in many areas of mathematics, physics, and engineering. In mathematics, determinants are used to solve systems of linear equations, and they have many applications in statistics, graph theory, and cryptography.

In physics, determinants are used to describe the properties of spacetime and the behavior of particles and fields. In engineering, determinants are used to design and analyze structures, such as bridges and buildings.

Etymology

The word “determinant” comes from the Latin “determinare”, meaning “to determine”, and it was first used in the 17th century to describe the value resulting from an algebraic operation.

Usage Notes

In mathematics, the word “determinant” is often used as a noun or a verb, and it can be used in a formal or informal setting. It is important to use the correct notation and terminology when discussing determinants, especially in an academic or professional context.

Cultural References

Determinants have been referenced in popular culture, such as in the TV show “The Big Bang Theory”, where the main characters often use mathematical concepts, including determinants, to solve problems.

Idiomatic Expressions or Phrases

“The determinant of a matrix is not always defined”

Related Words or Phrases

Eigenvalue

Linear transformation

Matrix

Collocations

“determinant matrix”

“determinant of a linear transformation”

Frequency of Use

Determinants are used frequently in mathematics, physics, and engineering, and it is important to understand the concept and notation when working with them.

Common Misspellings

• Determinent
• Determint
• Determinnat