On the Formal Differentiation of Traces and Determinants

Bibliographic Data

ID19291663
AuthorsPeter H Schonemann (corresponding author)
Year1985
Volume20
Issue2
Pages113-139
Publication date1985-04-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueMultivariate Behavioral Research (JOURNAL)
Journal identifiersISSN: 0027-3171 • E-ISSN: 1532-7906
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1207/s15327906mbr2002_1
PMID26771405
OpenAlexW2033711720
LanguageEN
Citations received2
References cited22

A compact notation for obtaining and handling matrices of partial derivatives is suggested in an attempt to generalize "symbolic vector differentiation" to matrices of independent variables. The proposed technique differs from methods advocated by Dwyer and MacPhail (1948) and Wrobleski (1963) in several respects, notably in a deliberate limitation on the classes of scalar functions considered: traces and determinants. To narrow interest to these two classes of scalar matrix functions allows one to invoke certain algebraic identities which simplifies the problem, because (a) the treatment of traces of products of matrices can be reduced to that of a few representatives of large equivalence classes of such products, all having the same formal derivative, and because (b) the more involved task of differentiating determinants of matrix products can be translated into the more amenable problem of differentiating the traces of such products. A number of illustrative examples are included in an attempt to show that the above limitation is not as serious as might at first appear, because traces and determinants apply to a wide range of psychometric and statistical problems

Algebra over a field · Algebraic number · Arithmetic · Equivalence (formal languages) · Matrix (chemical analysis) · Notation · Pure mathematics · Range (aeronautics) · Scalar (mathematics) · Vector space · Computer Science · Mathematics · Sensory Analysis and Statistical Methods · Theoretical Computer Science

Tools

Open DOISci-Hub