Accession Number:

AD0431018

Title:

NORMS AND CONDITION NUMBERS

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA

Personal Author(s):

Report Date:

1964-02-01

Pagination or Media Count:

17.0

Abstract:

The condition number c phi of a non-singular matrix A is defined by c phiA phiAphiA-1, where ordinary phi is a norm. It is known that for certain norms, the matrix AA is more illconditioned than A, i.e., c phiA is lesser than c phiAA. We prove that this inequality holds whenever the norm phi is unitarily invariant phiA is a function of the characteristic roots of AA. However, we show that the inequality is independent of the usual norm axioms. Some more general inequalities are also obtained.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE