We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular cases of interest such as the case when we have a spectral decomposition $A=UDU^{-1}$, the spectrum cut-off $C=A_+$ and the Nearest Correlation Matrix routine. Finally, we explain how to simplify the computation of adjoints for regularized linear regression coefficients.

翻译：我们为表格$C=f(A)$的正方形操作得出一个公式,其中美元在每一电子元值附近是全方位的。然后我们应用该公式来得出封闭式表达式,特别是在我们有一个光谱分解 $A=UDU}-1美元、频谱截断 $C=A*$和近距离相关矩阵常规等情况中。最后,我们解释如何简化正常线性线性回归系数的连接计算。