# Reverse Order Law for Generalized Inverses with Indefinite Hermitian Weights

@inproceedings{Kamaraj2021ReverseOL, title={Reverse Order Law for Generalized Inverses with Indefinite Hermitian Weights}, author={K. Kamaraj and P. S. Johnson and Athira Satheesh}, year={2021} }

The reverse order law for generalized inverse plays an important role in the theoretic research and numerical computations in many areas, including the singular matrix problems, ill-posed problems, optimization problems, and statistics problems (see, for instance, [1, 4, 7, 10, 9, 13, 6]). A classical result of Greville [12] gives necessary and sufficient conditions for the two term reverse order law for the Moore-Penrose inverse in the Euclidean space. It is known that the reverse order law…

## References

SHOWING 1-10 OF 22 REFERENCES

### A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse

- Mathematics
- 1974

Suppose the complex matrix M is partitioned into a $2 \times 2$ array of blocks; let $M_{11} = A,M_{12} = B,M_{21} = C,M_{22} = D$. The generalized Schur complement of A in M is defined to be $M/A =…

### Block generalized inverses

- Mathematics
- 1976

The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring R. A technique is developed for computing conditional and reflexive inverses for matrices in R2×2, which is…

### Indefinite Linear Algebra and Applications

- Mathematics
- 2005

Preface.- 1. Introduction and Outline.- 2. Indefinite Inner Products.- 3. Orthogonalization and Orthogonal Polynomials.- 4. Classes of Linear Transformations.- 5. Canonical Forms.- 6. Real…

### Moore-Penrose inverse in an indefinite inner product space

- Mathematics
- 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are…

### Inverse Order Rule for Weighted Generalized Inverse

- Mathematics
- 1998

The weighted generalized inverses have several important applications in researching the singular matrices, regularization methods for ill-posed problems, optimization problems, and statistics…

### Moore-Penrose inverse in indefinite inner product spaces

- Mathematics
- 2017

We present the denition and some properties for the Moore-Penrose inverse in possibly degenerate indenite inner product spaces. The extensions of appropriate results, given for matrices in Euclidean…

### Reverse order law of group inverses of products of two matrices

- MathematicsAppl. Math. Comput.
- 2004