How Do You Spell ADJOINT?

Pronunciation: [ɐd͡ʒˈɔ͡ɪnt] (IPA)

Adjoint is a mathematical term that refers to a matrix that is the transpose of its cofactor matrix. The spelling of this word is influenced by its French origin, where it is spelled as "adjointe". The IPA phonetic transcription of "Adjoint" is /əˈdʒɔɪnt/, phonetically represented as "uh-join-t". The first syllable "ad" is pronounced as "uh" with a schwa sound, followed by the "join" with a long "oi" sound, and ending with a soft "t" sound at the end.

ADJOINT Meaning and Definition

1. Adjoint is a mathematical term that can refer to different concepts depending on the specific field of study. In linear algebra, the adjoint is a concept related to matrices. Given a square matrix A, its adjoint, denoted as A*, is the matrix obtained by taking the complex conjugate of its transpose. In other words, the entry in the i-th row and j-th column of the adjoint matrix is the complex conjugate of the entry in the j-th row and i-th column of the original matrix. The adjoint matrix plays a crucial role in various applications, such as solving systems of linear equations, determining eigenvalues and eigenvectors, and calculating matrix inverses.

   In functional analysis, the adjoint refers to a linear map between two vector spaces that preserves certain properties. If A is a linear map from a vector space V to another vector space W, then the adjoint of A, denoted as A*, is a linear map from W* (the dual space of W) to V* (the dual space of V). The adjoint map satisfies a specific property, known as the adjoint property, which relates the duality between the two spaces. This concept is extensively used in the field of functional analysis to study operators on Hilbert spaces and other related structures.

   Overall, "adjoint" can refer to either a matrix or a linear map, both of which involve operations such as transposing, taking complex conjugates, and preserving certain properties between vector spaces.

Common Misspellings for ADJOINT

• zdjoint
• sdjoint
• wdjoint
• qdjoint
• asjoint
• axjoint
• acjoint
• afjoint
• arjoint
• aejoint
• adhoint
• adnoint
• admoint
• adkoint
• adioint
• aduoint
• adjiint
• adjkint
• adjlint
• adjouint
• adjont
• adjuent
• bckjoint
• abjoit
• abjoing
• abjoind
• Adjumint
• Adjoints
• Abjointe

Etymology of ADJOINT

The word "adjoint" in English can be traced back to the Latin word "adiunctus", which means "to join" or "to attach". This Latin term is derived from the prefix "ad-" meaning "to" or "toward", and the verb "iungere", meaning "to join" or "to yoke". Over time, the term "adiunctus" evolved into "adjoint" in English, retaining its fundamental meaning of something that is joined or attached. In specific mathematical contexts, the term "adjoint" refers to a particular type of operation or matrix that is related to the original operation or matrix.

Similar spelling words for ADJOINT

• self-adjoint,
• sub-adjoint,
• Adjoined.