The word adjugate is a term that is not commonly used in everyday language. It is a technical term that is mainly used in mathematics and other related fields. In this article, we will explore the definition and meaning of adjugate, its origin, and its use in different dictionaries.
Definitions
The adjugate is a mathematical term that refers to the transpose of the cofactor matrix of a square matrix. It is also known as the classical adjoint or the adjoint matrix. The adjugate of a matrix is obtained by replacing the elements of the matrix with their corresponding cofactors and then taking the transpose of the resulting matrix.
In legal terms, adjugate means to give a judgment or decision in a legal case. It is a term used in the context of a court of law, where a judge or jury is responsible for making a decision on a case.
Origin
The word adjugate comes from the Latin word “adjudicare,” which means to judge or decide. The word was first used in the context of mathematics in the 18th century.
Meaning in different dictionaries
In the Oxford English Dictionary, adjugate is defined as “to adjudicate or give a judgment in a legal case.” In the context of mathematics, it is defined as “the transpose of the cofactor matrix of a square matrix.”
Merriam-Webster defines adjugate as “the transpose of the matrix whose elements are the cofactors of the corresponding elements of a given square matrix.”
Associations
The term adjugate is mainly associated with mathematics, specifically linear algebra. It is used to calculate the inverse of a matrix and to solve systems of linear equations.
In legal terms, adjugate is associated with the legal system, where it is used to refer to the process of making a judgment or decision on a case.
Synonyms
The synonyms of adjugate include adjudicate, judge, decide, and arbitrate.
Antonyms
The antonyms of adjugate include vacate, overturn, and reverse.
The same root words
The word adjugate is derived from the Latin word “adjudicare,” which means to judge or decide. Other words derived from the same root include adjudicate, adjudication, and adjudicator.
Example Sentences
- The adjugate of a matrix is obtained by replacing the elements with their corresponding cofactors and then taking the transpose of the resulting matrix.
- The judge adjugated the case in favor of the plaintiff.
- The adjugate of a 3×3 matrix can be used to calculate its inverse.
- The court adjugated the dispute between the two parties and awarded damages to the plaintiff.
- The adjugate of a matrix is useful in solving systems of linear equations.