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How can I create dynamical matrices?

Posted 10 years ago

I'm trying to create dynamical matrices, i.e. whose variables/parameters depend explictly on time and where I can follow time evolution. First application was an economical system in matrix form..but couldn't sort out from manual and exemples how to make it work. Thanks for help

POSTED BY: Paolo Di Marco
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It looks like you have in mind a function that takes a matrix and some vectors and produces a new matrix. Then you want to iterate that construction. If you provide same input (in Mathematica input form) and the desired result or at least after one step, then maybe more can be suggested about how to go about this.

POSTED BY: Daniel Lichtblau

Thanks to both, actually I was too sketchy: my system would look like this : Apß=Bp, with A and B square matrices, p vector and ß single variable. (A and B are like Leontiev input/output matrices) Left term is at the beginning of first cycle, right one at the end. The elements of A are given at the beginning, the ones in B are calculated from those in A (following some rules and conditions). p is supposed to be a unique solution, together with ß, that satisfies all preconditions. On second cycle A changes (using the values of B..), so will as a consequence p ( ß too should). And so on..

So we don't have explicit dependance on a continuos time, but a sequence of matrices (A(t) , with t discrete). I couldn't find out how to write this process.

POSTED BY: Paolo Di Marco


m[t_] := {{t, t^2, Cos[t]}, {2, Sin[t], 3}, {3 t, Tan[t], -t}};
m[t] // MatrixForm

enter image description here

Plot[{Abs[Eigenvalues[m[t]]]}, {t, -3, 3}, PlotTheme -> "Marketing"]

enter image description here

POSTED BY: Vitaliy Kaurov

Perhaps a more specific example would help. What you seem to describe is simply a matrix that is a function of time. That is simple to do.

Here is a rotation matrix that depends on time:

{{Cos[t], -Sin[t]}, {Sin[t], Cos[t]}}
POSTED BY: David Reiss
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