NORMS AND CONDITION NUMBERS

Abstract

The condition number c phi of a non-singular matrix A is defined by c phi(A) = phi(A)phi(A(-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 phi(A) is lesser than c phi(AA*). We prove that this inequality holds whenever the norm phi is unitarily invariant (phi(A) 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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1964
Accession Number
AD0431018

Entities

People

  • Albert W. Marshall
  • Ingram Olkin

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Algebra
  • Eigenvalues
  • Government Procurement
  • Governments
  • Inequalities
  • Linear Algebra
  • Mathematics
  • Permutations
  • Procurement
  • Scientific Research
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Naval Engineering and Maritime Security