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

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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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