Re: Numerical Determinants

*To*: mathgroup at smc.vnet.net*Subject*: [mg13001] Re: Numerical Determinants*From*: hello at there.com (Rod Pinna)*Date*: Tue, 30 Jun 1998 00:26:01 -0400*Organization*: UWA*References*: <6n4o6m$nin@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Thanks for the reply. I eventually realised that I should be using the eigenvalue function, however, it turns out that for the matricies I'm examining, B is non-invertible. To get around this, I've been using the following: 1 -------------------------- Eigenvalues[Inverse[A]].B] This seems to be giving me the expected answers for A.x=p B.x, However, I'm not convinced by the mathematics of it... Thanks again though. In article <6n4o6m$nin at smc.vnet.net>, Hugh Walker <hwalker at gvtc.com> wrote: >Yes, I have a suggestion. Consider the eigen-problem -a.x = p b.x. >Non-trivial eigenvectors exit provided Det[a + b p] = 0, which is your >situation. Assuming Inverse[b] exists, the eigen values of m.x = p x >where m = -Inverse[b].a > >Eigenvalues[-Inverse[b].a] > >will coincide with your p's. > >I tested cases in which a and b are each random 10x10 matrices. The >results were the same, and timings for the two approaches were > >Det = 9.0 sec >eigen = 0.0 sec > >I hope this helps. > > >Hugh Walker >Professsor Emeritus >University of Houston > >Gnarly Oaks > > Rod Pinna (rpinnaX at XcivilX.uwa.edu.au Remove the X for email)