Accession Number : AD0431018


Title :   NORMS AND CONDITION NUMBERS


Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA


Personal Author(s) : Marshall, Albert W ; Olkin, Ingram


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/431018.pdf


Report Date : Feb 1964


Pagination or Media Count : 17


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.


Descriptors :   *INEQUALITIES , FUNCTIONS(MATHEMATICS) , MATRICES(MATHEMATICS) , NUMBER THEORY , NUMBERS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE