Expression of a Real Matrix as a Difference of a Matrix and its Transpose Inverse

Abstract

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of transpose-inverse terms prove to be obstacles, particularly in control theory and related applications such as computational simulation and analysis of matrix representations of articulated figures.

References in corpus (3)

• Articulated Shape Matching Using Laplacian Eigenfunctions and Unsupervised Point Registration
• On the Relative Gain Array (RGA) with Singular and Rectangular Matrices
• A Rank-Preserving Generalized Matrix Inverse for Consistency with Respect to Similarity

Cited by in corpus (2)

• On Radically Expanding the Landscape of Potential Applications for Automated Proof Methods
• On Use of the Moore-Penrose Pseudoinverse for Evaluating the RGA of Non-Square Systems