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## Re: minors and cofactors

**From**: |
johan19 |

**Subject**: |
Re: minors and cofactors |

**Date**: |
Fri, 18 Sep 1998 17:30:58 -0400 |

On Fri, Sep 18, 1998 at 06:44:39PM +0200, Dirk Laurie wrote:
>* Thanks to David Clark for a fascinating question. I keep getting*
>* new thoughts after having posted two answers, but this is the last*
>* one.*
>* *
>* There is a fully satisfactory way of calculating the cofactor matrix*
>* that requires no rank decision.*
>* *
>* Calculate the SVD A=U*S*V'.*
>* Then det(A)=det(U)*det(S)*det(V')*
>* and inv(A)=V*inv(S)*U'.*
>* Hence inv(A)*det(A) = (det(V')*V) * (det(S)*inv(S)) * (det(U)*U')*
>* The middle factor can be calculated by replacing each diagonal term*
>* be the product of the others.*
just to throw my two cents in...
note that U and V in the SVD are *unitary* matrices and hence have
det(U)=det(V)=1. S is diagonal hence the determinant is trivial to
compute.
simpleton's (that'd be me) wild-ass guess, is the cofactor related to
deleting a row from both U and V and forming the product Uk*S*Vk' or
Vk*S*Uk' where Uk and Vk are U and V missing row k?
(i'd check myself, but i haven't been able to recompile octave 2.1.7
since upgrading to egcs-1.1 and the new libstdc++ isn't compatible.
unfortunately, i blew away my old libstdc++ so i guess it may be a day
or two before i get a working one again...)
--
Johan Kullstam address@hidden Don't Fear the Penguin!