ADJUGATE Meaning and
Definition
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Adjugate is an adjective that is commonly used in mathematics and geometry to describe a particular type of matrix, determinant, or complex number. The word derives from the Latin "adjugatus," which means "awarded" or "assigned."
In mathematics, an adjugate matrix refers to the transpose of a cofactor matrix of a square matrix. The cofactor matrix is obtained by taking the determinant of each minor matrix formed by deleting a row and a column from the original matrix. The adjugate matrix is obtained by transposing this cofactor matrix.
Similarly, the adjugate determinant is the determinant of the adjugate matrix. It is obtained by taking the determinant of the transpose of the cofactor matrix.
In complex analysis, the adjugate of a complex number is obtained by taking the complex conjugate of the number. This involves changing the sign of the imaginary part while keeping the real part unchanged.
The concept of adjugate is important in various mathematical applications, such as finding the inverse of a matrix, solving systems of linear equations, and computing complex roots of polynomials. It allows for simplification and manipulation of mathematical expressions and assists in solving complex problems.
Common Misspellings for ADJUGATE
Etymology of ADJUGATE
The word adjugate has a Latin origin. It comes from the Latin verb adiudico which means to assign or allot. The Latin word adjugatum is the past participle of adiudico and meant awarded or assigned. Over time, this Latin word evolved into adjugate in English, which generally means to pronounce or declare by a judicial decision.
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