A NOTE ON SEMIDEFINITE MATRICES

reportActive / Technical Report | Accession Number: AD0267584 | Open PDF

Abstract:

It is of general interest to find criteria for a matrix to be positive or negative- semidefinite. The usual characterization of semidefinite matrices in terms of their principal minors can be rather laborious to implement practically. An elementary proof of a known alternate characterization of a semidefinite matrix in terms of its null-space and of its largest characteristic value is presented. An iterative procedure is also suggested which may be useful in deciding the semidefiniteness of a matrix.

Author(s):
Eisenberg, Edmund
Author Organization(s):
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
Supplementary Note:
DOI: 10.21236/AD0267584
Pagination:
0017

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
RR-9, IER-172-10
Contract/Grant Number(s):
NONR-222-83
Monitor Series:
ONR
 Subject Terms
Joint Capability Areas:
JCA_1_Force Support; JCA_1.3_Human Capital Management; JCA_1.3.2_Personnel Management; JCA_1.2_Force Preparation
Communities of Interest:
No COI(s) Identified
Descriptor(s):
*MATRICES(MATHEMATICS), *STATISTICAL TESTS, POLYNOMIALS, STATISTICAL ANALYSIS, TRANSFORMATIONS(MATHEMATICS)
Field(s)/Group(s):
Numerical Mathematics
Report Date:
1961 Jul 20