Characterizations of Weighted Matrix Inverses
Analysis
This paper explores properties and characterizations of W-weighted DMP and MPD inverses, which are important concepts in matrix theory, particularly for matrices with a specific index. The work builds upon existing research on the Drazin inverse and its generalizations, offering new insights and applications, including solutions to matrix equations and perturbation formulas. The focus on minimal rank and projection-based results suggests a contribution to understanding the structure and computation of these inverses.
Key Takeaways
- •Revisits and extends the study of W-weighted DMP and MPD inverses.
- •Provides new characterizations and equivalent properties.
- •Applies results to solve matrix equations and derive perturbation formulas.
- •Focuses on minimal rank and projection-based results.
- •Establishes reverse and forward order laws using W-weighted weak Drazin inverse.
Reference
“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”