A HOL Theory of the Differential for Matrix Functions

Abstract

The differential of matrix functions(DMF) plays an important role in mathematics and engineering. Common applications of it are found in optimization analysis, computer vision, robotics, etc. In this paper, a formal method based on HOL is used to construct the DMF based on Fréchet differential in matrix space. In order to illustrate the practical effectiveness of our work, we use our formalization to verify a property of matrix exponential.