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On the Adjoint Matrix

dc.contributor.authorStewart, G. W.en_US
dc.description.abstractThe adjoint $A\adj$ of a matrix $A$ is the transpose of the matrix of the cofactors of the elements of $A$. The computation of the adjoint from its definition involves the computation of $n^{2}$ determinants of order $(n-1)$\,---\,a prohibitively expensive $O(n^{4})$ process. On the other had the computation from the formula $A\adj = \det(A)A\inv$ breaks down when $A$ is singular and is potentially unstable when $A$ is ill-conditioned. In this paper we first show that the ajdoint can be perfectly conditioned, even when $A$ is ill-conditioned. We then show that if due care is taken the adjoint can be accurately computed from the inverse, even when the latter has been inaccurately computed. In an appendix to this paper we establish a folk result on the accuracy of computed inverses. \end{minipage} \end{center} Also cross-referenced as UMIACS-TR-98-02en_US
dc.format.extent164081 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3864en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-98-02en_US
dc.titleOn the Adjoint Matrixen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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