TY - JOUR
T1 - On the adjugate matrix
JF - Linear Algebra and its Applications
Y1 - 1998
A1 - Stewart, G.W.
AB - The adjugate AA of a matrix A is the transpose of the matrix of the co-factors of the elements of A. The computation of the adjugate from its definition involves the computation of n2 determinants of order (nā1)āa prohibitively expensive O(n4) process. On the other hand, the computation from the formula AA = det (A)Aā1 breaks down when A is singular and is potentially unstable when A is ill-conditioned with respect to inversion. In this paper we first show that the adjugate can be perfectly conditioned, even when A is ill-conditioned. We then show that if due care is taken the adjugate can be accurately computed from the inverse, even when the latter has been inaccurately computed. In Appendix A we give a formal derivation of an observation of Wilkinson on the accuracy of computed inverses.
VL - 283
SN - 0024-3795
UR - http://www.sciencedirect.com/science/article/pii/S0024379598100988
CP - 1ā3
M3 - 10.1016/S0024-3795(98)10098-8
ER -