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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
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