ScholarLens Back to search
1988•SIAM Journal on Matrix Analysis and ApplicationsRequires access

Linear Preservers of the Class of Hermitian Matrices with Balanced Inertia

Stephen Pierce, Leiba Rodman

Open publisher page 10 citations

Abstract

Let $H ( n )$ the $n^2 $-dimensional real vector space of Hermitian matrices. Assume n is even and greater than or equal to 4. Let T be an invertible linear transformation on $H ( n )$ that maps the class of invertible, balanced inertia (signature zero) Hermitian matrices into itself. Then for some real number $c \ne 0$, and an invertible matrix $S,T ( A ) = cS^* AS$ or $T ( A ) = cS^* A^T S$, for all $A \in H( n )$. T is also classified in the case where $n=2$.

About this research paper

What this paper is about

Let $H ( n )$ the $n^2 $-dimensional real vector space of Hermitian matrices. Assume n is even and greater than or equal to 4. Let T be an invertible linear transformation on $H ( n )$ that maps the class of invertible, balanced inertia (signature zero) Hermitian matrices into itself. Then for some real number $c \ne 0$, and an invertible matrix $S,T ( A ) = cS^* AS$ or $T ( A ) = cS^* A^T S$, for all $A \in H( n )$. T is also classified in the case where $n=2$.

Why it matters

OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let $H ( n )$ the $n^2 $-dimensional real vector space of Hermitian matrices. Assume n is even and greater than or equal to 4. Let T be an invertible linear transformation on $H ( n )$ that maps the class of invertible, balanced inertia (signature zero) Hermitian matrices into itself. Then for some real number $c \ne 0$, and an invertible matrix $S,T ( A ) = cS^* AS$ or $T ( A ) = cS^* A^T S$, for all $A \in H( n )$. T is also classified in the case where $n=2$.

Key concepts: Invertible matrix, Hermitian matrix, Mathematics, Combinatorics, Linear map, Vector space, Matrix (chemical analysis), Class (philosophy)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Linear Preservers of the Class of Hermitian Matrices with Balanced Inertia — Research Paper | ScholarLens