The relationship of inertias between two representations of linear subspaces

Abstract

This work gives complete expressions of inertia of matrices involved in a linear subspace of ${\mathbb{R}}^n\times {\mathbb{R}}^n$ when they are presented in two different ways, specifically, as image and as well as kernel of linear maps.

Keywords:

• Linear subspace
• monotone sets
• inertia of a matrix

2010 Mathematics Subject Classifications:

• 15A18
• 47H05
• 54C60

Acknowledgments

The authors thank the corresponding editor and two anonymous referees for their helpful suggestions for improving this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.