“adjoint(of a matrix)”的概念、定义、翻译、参考文献-科学参考

adjoint(of a matrix)

Mathematics

单词	adjoint(of a matrix)
释义	adjoint(of a matrix) Mathematics The adjoint of a square matrix A, denoted by adjA, is the transpose of the matrix of cofactors of A. For A=[a_ij], let A_ij denote the cofactor of the entry a_ij. Then the matrix of cofactors is the matrix [A_ij] and adj A=[A_ij]^T. For example, a 3×3 matrix A and its adjoint can be written $A = [\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}], adj A = [\begin{matrix} A_{11} & A_{21} & A_{31} \\ A_{12} & A_{22} & A_{32} \\ A_{13} & A_{23} & A_{33} \end{matrix}] .$ In the 2×2 case, a matrix A and its adjoint has the form $A = [\begin{matrix} a & b \\ c & d \end{matrix}], adj A = [\begin{matrix} d & - b \\ - c & a \end{matrix}] .$ 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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