# 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