Block-defined matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg15950] Block-defined matrices*From*: Roberto Pratolongo <rp at 3bt.imag.ge.cnr.it>*Date*: Wed, 17 Feb 1999 23:34:11 -0500*Sender*: owner-wri-mathgroup at wolfram.com

Dear MathGroupers, 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] ? My first efforts gave me the confirm that (at least for eigenvalues of block-symmetric M's) a close connection really exists, say: if A+2B is an eigenvalue of M when A,B are numbers, then Eigenvalues[A+2B] is a subset of Eigenvalues[M] when A,B are square blocks. But I was not able to manage this problem in the way described above, only by testing the conjecture for small matrices. My general problems, such Inverse[M] are *not* so simple. Maybe/probably such algebraic problems were resolved 150 years ago, but I don't know where to find more. Hoping to have been clear, I need help, please... Roberto Pratolongo EMAIL rp at imag.ge.cnr.it ***************************************************************** Roberto Pratolongo rp at imag.ge.cnr.it c/o IMAG - CNR Fax.+39-010-6475880 Via dei Marini, 6 16149 Genova (Italy) Tel.+39-010-6475873 *****************************************************************