“adjoint”的概念、定义、习题解题方法及翻译-数学辞典

单词

adjoint

释义

adjoint

(adjugate) (of a matrix) The adjoint of a square matrix A, denoted by adjA, is the transpose of the matrix of cofactors of A. For A=[aij], let Aij denote the cofactor of the entry aij. Then the matrix of cofactors is the matrix [Aij] and adj A=[Aij]^T. For example, a 3×3 matrix A and its adjoint can be written

In the 2×2 case, a matrix A and its adjoint has the form

The adjoint is important because it can be used to find the inverse of a matrix. From the properties of cofactors, it can be shown that AadjA=(detA)I. It follows that, when detA ≠ 0, the inverse of A is (1/detA) adjA.

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