Bott-Duffin group inverse
Xiangyu Zhang, Kezheng Zuo, Jing Zhou · Linear and Multilinear Algebra · 2025
This paper introduces the Bott-Duffin group inverse of a square matrix with respect to a subspace, which extends the Bott-Duffin inverse. We further give some of its properties, characterizations and representations by the PL-decomposition. In addition, we consider the application of the Bott-Duffin group inverse in solving a class of restricted linear equations in electrical network theory. Finally, the Bott-Duffin group inverse is applied to solve the other two classes of restricted linear equations, and the Cramer's rule for their unique solutions has also been discussed.