Vol. 49, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Definite and semidefinite matrices in a real symmetric matrix pencil

Frank Uhlig

Vol. 49 (1973), No. 2, 561–568
Abstract

Pencils that contain a definite matrix (d-pencils) have been characterized in several ways. Here d-pencils will be characterized by the property of the set L = {(ai,bi)}R2 if S and T are simultaneously congruent to diag (ai) and diag (bi), respectively. This way one can describe all definite and semidefinite matrices in a d-pencil. Similarly one can characterize all pencils that contain semidefinite but no definite matrices (s.d. pencils). The explicit condition on L for d-pencils is then used to reprove the theorem that two real symmetric matrices generate a d-pencil iff their associated quadratic forms do not vanish simultaneously.

Mathematical Subject Classification 2000
Primary: 15A48
Milestones
Received: 12 July 1972
Published: 1 December 1973
Authors
Frank Uhlig