Re: Block-defined matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg16005] Re: Block-defined matrices*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Sat, 20 Feb 1999 02:52:00 -0500*Organization*: University of Western Australia*References*: <7ag4sj$b1d@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Roberto Pratolongo wrote: > I've a problem of matrix algebra. I want to commonly manage > matrices(calculate their inverse,determinant,etc.): they are symbolically > defined by square blocks. > For example, let M ={{A,B},{C,D}}, where A,B,C,D are 3x3 blocks. > > So, it exists a way to obtain the output of e.g. Inverse[M] described in > terms of > A, Inverse[A], B, Inverse[B], C, Inverse[C], D, Inverse[D] ? It is not too hard to show (by hand) that, if A,B,C,D are invertible, the inverse can be written in the form, {{Inverse[A - B.Inverse[D].C], Inverse[C - D.Inverse[B].A]}, {Inverse[B - A.Inverse[C].D], Inverse[D - C.Inverse[A].B]}} If, e.g., D is not invertible then the [[1,1]] entry of the inverse can be replaced by -Inverse[C].D.Inverse[B-A.Inverse[C].D] etc. I am not aware of any general Mathematica tools for performing such operations though ... Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________