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Solving matrix equation using Solve?

Anton Nakov, ECB
Posted 3 years ago
POSTED BY: Anton Nakov
3 Replies
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That is nonlinear and with symbolic parameters, good luck!
POSTED BY: Gianluca Gorni
Anton Nakov
Anton Nakov, ECB
Posted 3 years ago

Thanks a lot, that's very useful!!

The problem I am trying to solve is listed below, it says "running", hopefully it works also with symbols Where beta kappa sigma theta are all real numbers.

A11 = {{\[Beta] + \[Kappa]/\[Sigma], \[Kappa]}, {1/\[Sigma], 1}};
A21 = {{\[Theta]/(\[Sigma] . \[Sigma]) - \[Kappa]/\[Sigma] - \[Beta], \
\[Theta]/\[Sigma] - \[Kappa]}, {\[Beta] . \[Theta]/(\[Sigma] . \
\[Sigma]), \[Beta] . \[Theta]/\[Sigma]}};
A22 = {{1 + \[Kappa]/\[Sigma], 
    1}, {\[Beta] . \[Kappa]/\[Sigma], \[Beta]}};
Solve[A11 . c == c . A21 . c + c . A22 && 
  Element[c, Matrices[{2, 2}]], c]
POSTED BY: Anton Nakov

You can declare that your variable c is a matrix:

A11 = RandomInteger[{-3, 3}, {2, 2}];
A22 = RandomInteger[{-3, 3}, {2, 2}];
A21 = RandomInteger[{-3, 3}, {2, 2}];
Solve[A11 . c == c . A21 . c + c . A22 && 
  Element[c, Matrices[{2, 2}]], c]
POSTED BY: Gianluca Gorni
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