Mathematica:Matrix Multiplication of five 6x6 matrices

[parazit]

Hi,
I have five 6x6 matrices defined on mathematica with some unknowns and I need the final matrix let's say, mf.

When I tried to find out mf with Dot[] command, it works but the result won't be so logic. On the other hand, when I tried to do this multiplication with . symbol, there exists a result but when I asked the program let's say mf[[1,1]] it prints the entire row.

Lets say my matrices are m1,m2,m3,m4 and m5.( Notation is just for assumption)

What should I do to calculate if mf is written like following on the paper;
mf=m1.m2.m3.m4.m5

I tried a way like this also,

aa=m5.m4;
bb=aa.m3;
cc=bb.m2;
mf=cc.m1;

However, this is not logic. There sould be some way to define more than 2 matrices multiplication in one time.

If you need or request, I can upload my studies too.

Best.

 

[Hepth]

What do you mean by so logic? Can you attach an example mathematica file?

for me m1.m2.m3 works fine. Or try m1.(m2.m3) to force order of operations.

 

[parazit]

I mean the result is not so useful for further calculations.

I am trying to calculate the sf value that shown on the Dsf matrix. To do that I need to multiply that five 6x6 matrice and than use the Ts[[1,2]]=0 and Ts[[3,4]]=0 statements to find βex. After that, I can calculate sf. βex also sf must be some meanfull result compared to the reference values.

For example, If I take βin=βex=0 than ψin=ψex=0.001939 rad and than alpha will be 90 degree which is also 1.57 rad. From there,ρ will be 0.075 m. The other variables will not change. Than when I made the calculations I got sf as positive and negative two values however it should have a single, small, positive value.

I am so so confused even this is just a simple problem...

 

[Bill Simpson]

Ts = Dsi.Medgein.Mbody.Medgeex.Dsf // MatrixForm

is not doing a matrix multiply
then assigning that matrix to TS
THEN changing the result into MatrixForm to display it.

Instead it
is doing a matrix multiply
then changing the result into MatrixFormwhich is different from a matrix
THEN assigning that to to Ts and finally displaying that.

Instead of this
Ts = Dsi.Medgein.Mbody.Medgeex.Dsf // MatrixForm
Ts[[1, 2]]
Ts[[3, 4]]
do this
Ts = Dsi.Medgein.Mbody.Medgeex.Dsf;
Ts // MatrixForm
Ts[[1, 2]]
Ts[[3, 4]]

See if your results are meaningful after this change

 

[parazit]

Thank you Bill Simpson, it worked for the matrix multiplication.

Then I tried to solve the rest that I mentioned. If you don't mind please share the results if it's possible. I would like to compare them with mine and try to find a way.

Thank you.

 

[Bill Simpson]

Using your multiplication.nb notebook that you posted with this small change:
...
Ts = Dsi.Medgein.Mbody.Medgeex.Dsf
Ts // MatrixForm
Ts[[1, 2]]
Ts[[3, 4]]
FindRoot[{Ts[[1, 2]] == 0, Ts[[3, 4]] == 0}, {{βex, 0}, {sf, 1}}]

returns

{βex -> 0.135322, sf -> -0.258422}

Since you have trig functions there will be many solutions for βex.

For example, this shows the repeating solutions for both equations for repeating values of βex given a fixed value for sf:

Plot[Evaluate[{Ts[[1, 2]], Ts[[3, 4]]} /. sf -> -0.2584215664919408], {βex, -2 Pi, 2 Pi}]

I have not explored whether there are other values of sf which yield solutions, but I would not be surprised if there were whole parametric curves for values of {βex, sf} that are solutions to your pair of equations.

Note: It is dangerous and error prone to not use a semicolon between each expression in a notebook. Sometimes you can do this and still have it work. But this has been a source of difficult to track down errors for many years. I suggest ending each expression in your notebook with a semicolon and using Print[] if you need to have an expression displayed when evaluating a notebook.

 

[parazit]

Bill Simpson,
Thank you so much for your advise and help. I know that the function is periodic but actually expect a small value for βex and also a small value for sf since the final result which I have to reach is multiplication of Ts[[1,1]] and 0.01 must be a positive and really really small number.

I will check the whole code today and rewrite it in a form that you mentioned. Also I will add some notes that indicates the meaning of each value.

Thank you so much for your kind and helpfull messages.