@article {17717, title = {On the adjugate matrix}, journal = {Linear Algebra and its Applications}, volume = {283}, year = {1998}, month = {1998/11/01/}, pages = {151 - 164}, abstract = {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 (n-1){\textemdash}a prohibitively expensive O(n4) process. On the other hand, the computation from the formula AA = det (A)A-1 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.}, isbn = {0024-3795}, doi = {10.1016/S0024-3795(98)10098-8}, url = {http://www.sciencedirect.com/science/article/pii/S0024379598100988}, author = {Stewart, G.W.} }