# ON GENERALIZED INVERSES OF BANDED MATRICES

@article{Bapat2007ONGI, title={ON GENERALIZED INVERSES OF BANDED MATRICES}, author={Ravindra B. Bapat}, journal={Electronic Journal of Linear Algebra}, year={2007}, volume={16}, pages={24} }

Bounds for the ranks of upper-right submatrices of a generalized inverse of a strictly lower k-banded matrix are obtained. It is shown that such ranks can be exactly predicted under some conditions. The proof uses the Nullity Theorem and bordering technique for generalized inverse.

## 3 Citations

### The Nullity Theorem, Its Generalization and Applications

- Mathematics
- 2015

The Nullity theorem says that certain pairs of submatrices of a square invertible matrix and its inverse (known as complementary submatrices) have the same nullity. Though this theorem has been…

### Group inverses of matrices with path graphs

- Mathematics
- 2008

A simple formula for the group inverse of a 2 × 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the…

## References

SHOWING 1-10 OF 12 REFERENCES

### Rank structure of generalized inverses of rectangular banded matrices*

- Mathematics
- 2005

We describe rank structures in generalized inverses of possibly rectangular banded matrices. In particular, we show that various kinds of generalized inverses of rectangular banded matrices have…

### The Interplay of Ranks of Submatrices

- MathematicsSIAM Rev.
- 2004

A banded invertible matrix T has a remarkable inverse. All "upper" and "lower" submatrices of T-1 have low rank (depending on the bandwidth in T). The exact rank condition is known, and it allows…

### Generalized inverses of linear transformations

- Mathematics
- 1979

Preface to the Classics edition Preface Introduction and other preliminaries 1. The Moore-Penrose or generalized inverse 2. Least squares solutions 3. Sums, partitioned matrices and the constrained…

### Generalized inverses: theory and applications

- Mathematics
- 1974

* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of…

### Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society

- Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society
- 2007