How to multiply two symbolic matrices fully?

I need multiply 2 matrices:

syms epsXX1 epsXX2 epsXY1 epsXY2 epsYY1 epsYY2 epsZZ1 epsZZ2;
eps = [epsXX1 - 1i*epsXX2, epsXY1 - 1i*epsXY2, 0; ...
  -(epsXY1 - 1i*epsXY2), epsYY1 - 1i*epsYY2, 0;
  0, 0, epsZZ1 - 1i*epsZZ2;];
syms muXX1 muXX2 muXY1 muXY2 muYY1 muYY2 muZZ1 muZZ2;
mu = [muXX1 - 1i*muXX2, muXY1 - 1i*muXY2, 0; ...
  -(muXY1 - 1i*muXY2), muYY1 - 1i*muYY2, 0;
  0, 0, muZZ1 - 1i*muZZ2;];
eps * mu

Result is follow,

[   (epsXX1 - epsXX2*1i)*(muXX1 - muXX2*1i) - (epsXY1 - epsXY2*1i)*(muXY1 - muXY2*1i),   (epsXY1 - epsXY2*1i)*(muXX1 - muXX2*1i) + (epsYY1 - epsYY2*1i)*(muXY1 - muXY2*1i, 0]
[ - (epsXX1 - epsXX2*1i)*(muXY1 - muXY2*1i) - (epsXY1 - epsXY2*1i)*(muYY1 - muYY2*1i), - (epsXY1 - epsXY2*1i)*(muXY1 - muXY2*1i) + (epsYY1 - epsYY2*1i)*(muYY1 - muYY2*1i), 0]
[0, 0, (epsZZ1 - epsZZ2*1i)*(muZZ1 - muZZ2*1i)]

but I need to get its in more simple form:

[(a + b + ..) + (a1 + b1 + ..)+1i, .., ..]
[(a + b + ..) + (a1 + b1 + ..)+1i, .., ..]
[(a + b + ..) + (a1 + b1 + ..)+1i, .., ..]

Is exist some ways to get this?

Answer 1

[Andreas Apostolatos]

Hi Igor,

I understand that you are seeking to have the components of the resulting matrix from the multiplication expanded. You can use function 'expand' for your needs, see the following documentation page accordingly,

https://www.mathworks.com/help/symbolic/sym.expand.html

This way, the operation 'expand(eps*mu)' results in the following expanded expression,

[epsXX1*muXX1 - epsXX2*muXX2 - epsXY1*muXY1 + epsXY2*muXY2 - epsXX1*muXX2*1i - epsXX2*muXX1*1i + epsXY1*muXY2*1i + epsXY2*muXY1*1i, epsXX1*muXY1 - epsXX2*muXY2 + epsXY1*muYY1 - epsXY2*muYY2 - epsXX1*muXY2*1i - epsXX2*muXY1*1i - epsXY1*muYY2*1i - epsXY2*muYY1*1i,                                                               0]
[epsXY2*muXX2 + epsXY1*muXX2*1i + epsXY2*muXX1*1i - epsXY1*muXX1 - epsYY1*muXY1 + epsYY1*muXY2*1i + epsYY2*muXY1*1i + epsYY2*muXY2, epsXY2*muXY2 + epsXY1*muXY2*1i + epsXY2*muXY1*1i - epsXY1*muXY1 + epsYY1*muYY1 - epsYY1*muYY2*1i - epsYY2*muYY1*1i - epsYY2*muYY2,                                                               0]
[                                                                                                                                0,                                                                                                                                 0, epsZZ1*muZZ1 - epsZZ2*muZZ2 - epsZZ1*muZZ2*1i - epsZZ2*muZZ1*1i]

I hope this helps.

Kind regards,

Andreas

[Igor Arkhandeev]

Hi Andreas, thanks so much!