AN INTRODUCTION OF MATRIX DERIVATIVES AND THEIR APPLICATIONS IN MODAL ANALYSIS

摘要

The matrix derivative is a useful mathematical tool for modal analysis and its applications. The information on matrix derivatives is sparse in the literature of modal analysis. This paper endeavours to provide a systematic introduction to matrix and vector derivatives. This includes matrix derivatives with respect to a scalar quantity, to elements of another vector/matrix, and derivatives of a scalar function with respect to a matrix. The paper then outlines some applications of matrix derivatives in modal analysis. Among them are applications on curve fitting, sensitivity analysis, analytical model updating, and orthogonality considerations of inaccurate mode shapes. It is hoped that this paper can provide useful information for modal analysts interested in matrix derivatives and applications.