We present the classical coordinate-free formalism for forward and backward mode ad in the real and complex setting. We show how to formally derive the forward and backward formulae for a number of matrix functions starting from basic principles.

翻译：我们在真实和复杂的环境中为前向和后向模式广告提出传统的无协调形式主义,我们展示了如何正式地从基本原则出发,为一些矩阵功能提出前向和后向公式。