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adjugate

Meanings

  • The adjugate of a square matrix is the transpose of the cofactor matrix.

    - "Find the adjugate of the following 3x3 matrix: [1, 2, 3], [4, 5, 6], [7, 8, 9]]"
Rhymes
Words rhyming with adjugate
adjugate , determinate , coefficient , evaluate
Homophones
Words having the same pronunciation but different meanings, origins, or spelling,

  1. adjugate

  2. adjudge

  3. adjudicate

Variants
List of all variants of adjugate that leads to same result
adjust , adjustabilities , adjustability , adjustable , adjusted , adjusting , adjustive , adjusts , re-adjust , re-adjusted , re-adjusting , re-adjusts , readjust , readjusted , readjusting , readjusts
Forms
Different forms of the word (e.g., verb conjugations, plural forms, comparative/superlative forms for adjectives).

The adjugate of a square matrix is a determinant that can be used to find the inverse of the matrix., The adjugate of a matrix is the transpose of its cofactor matrix., The adjugate of a matrix is a special determinant that can be used to find the inverse of the matrix., The adjugate of a matrix is a square matrix of the same size as the original matrix, whose determinant is equal to the absolute value of the determinant of the original matrix., The adjugate of a matrix is a determinant that can be calculated as the product of the cofactors of the given matrix, arranged in the same order as the original matrix, but with the diagonal elements replaced by the negatives of those elements., The adjugate of a matrix is a determinant that can be calculated as the product of the cofactors of the given matrix, arranged in the same order as the original matrix, but with the diagonal elements replaced by the negatives of those elements.

Etymology
origin and the way in which meanings have changed throughout history.

The term 'adjugate' comes from the Latin word 'adjudicatus', which means 'pronounced judgment upon'. In mathematics, the adjugate of a matrix is a determinant of a matrix that is used to find the inverse of the matrix.

Related Concepts
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  1. determinant: A determinant is a special number that can be calculated from the elements of a square matrix. The determinant can be used to find the inverse of a matrix, to find the eigenvalues of a matrix, and to determine whether a matrix is invertible or not.

  2. cofactor: A cofactor is an element of a square matrix that is used to calculate the determinant of the matrix. Each element of a square matrix has a corresponding cofactor, which is obtained by either multiplying the elements of the minor matrix that corresponds to the given element, or by subtracting the product of the elements of the minor matrix that corresponds to the position of the negative of the given element, from the product of the determinant of the minor matrix that corresponds to the given element, and the cofactor of the given element.

Culture
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The term 'adjugate' has been used in various fields, including mathematics, physics, and engineering. In mathematics, the adjugate of a matrix is used to find the inverse of the matrix. In physics and engineering, the adjugate of a system of linear equations is used to find the eigenvectors and eigenvalues of the system. The adjugate has also been used in statistics and econometrics to find the inverse of a covariance matrix. In popular culture, the term 'adjugate' may not be commonly known or used outside of mathematical, scientific, or technical contexts.

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