Matrix functions
- To: mathgroup at smc.vnet.net
- Subject: [mg42413] Matrix functions
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Sat, 5 Jul 2003 03:10:58 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
We can define functions of an nxn matrix M as (infinite) series and study their convergence using a suitable matrix norm and/or numerically. For example (1) 1/(1-M)=1 + M + M^2 + M^3 + ... (2) mExp[M_]:=1+ M/1! + M^2/2! + ... (3) mCos[M_]:=(mExp[I*M] + mExp[-I*M])/2 Question: Are there standard functions (within some package) of this kind available? If not, what would be the best way to define e.g. the exponential matrix function (2), i.e. how to terminate the series appropriately? Any comments and help welcome. Wolfgang