@shahid You have a new equation eq1.
Secondly, you cannot use [] instead of parentheses ().

Change that before attempting again. You may have to work harder after that.

@xhimi To see matrices or vectors with dimensions higher than 10 do:
interface( rtablesize= 16); #
to set it at 16. By using
interface( rtablesize= infinity);
all sizes will be shown.
###
You say that your code stops at m := nops(L);
The answer obviously should be 4 in your case.
##
What type of elements do your matrices have? If they have datatype=float there ought not be any problem.
If on the other hand your entries have symbolic values like names or exact expressions like sqrt(2) or sin(1) then you can easily run into problems.
Remember that to find the eigenvalues (and the eigenvectors) you have to find the roots of a polynomial of degree 16, which is impossible in general except numerically.

@Carl Love Well, you take the real part. The real part does become zero:

evalc(ex1(x,t,z));
          -1.132*10^11*exp(9.9*10^6*x)*cos(-1.95*10^6*z+2.98*10^15*t)

Thus it is zero where cos(-1.95*10^6*z+2.98*10^15*t)=0, i.e. for
-1.95000000*10^6*z+2.980000000*10^15*t = Pi/2+p*Pi, p any integer and for any x.

## Getting rid of large numbers makes this less confusing:
ex1:= (x,t,z)-> Re(-exp(x + I*(z-t)));
plots:-implicitplot3d(
     ex1(x,t,z), x= -10..0, t= 0..10, z= 0..10,
     axes= boxed, style= patchcontour, scaling= constrained, shading= z,
     grid= [20$3]
);

@xhimi Well, here is a way. I still make the matrices small so that results are easy to understand.

restart;
with(LinearAlgebra):
n:=5: #Using nxn matrices
## Taking just 3 matrices:
A:=RandomMatrix(n,datatype=float);
B:=RandomMatrix(n,datatype=float);
C:=RandomMatrix(n,datatype=float);
L:=[A,B,C]; #Putting the matrices in a list
LE:=[Eigenvectors]~(L): #Finding vectors of eigenvalues and corresponding matrices whose columns are eigenvectors
LE[1]; #Result for A
LEV:=map2(op,2,LE); #Leaving out the vectors of eigenvalues
LEV[1]; #Matrix of eigenvectors of A
seq(LEV[1][..,i],i=1..n); #Eigenvectors for A
m:=nops(L); #Number of matrices
IntersectionBasis([seq([seq(LEV[j][..,i],i=1..n)],j=1..m)]);

xhimi 0

You say that you have a bunch of matrices. Why not just find all the eigenspaces and then use IntersectionBasis in one call?

@Preben Alsholm  I tried to move your reply to my answer to where it belongs, but it appears as my reply.

xhimi 0  WROTE:

Thanks a lot!

 I have tried the intersection basis but I am not not able to have a procedure that does both processes at the same time, i.e., finding the eigenspace and then recursively intersecting. HELP PLEASE!

Could you give us an actual example? I don't quite understand what you are trying to say.

Obviously the equation LambertW(ln(s)) = ln(z) doesn't have s=1 as a solution generically, i.e unless z=1, since
eval(LambertW(ln(s)) = ln(z), s=1) returns 0=ln(z). So I see that as a bug.
It is strange that occasionally that error occurs.
I tried
for sym in {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,x,y,z} do solve({LambertW(ln(zz)) = ln(sym)}, zz) end do;
and didn't see any problems, though.
##Added: I also tried:
for sym in {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,t,u,v,x,y,z} do solve({LambertW(ln(s)) = ln(sym)}, s) end do;
which exhibited the error for sym= t,u,v,x,y,z.
It so happens that t,u,v,x,y,z all follow after s in the alphabet.
## Suspicion confirmed by now lettin g be the unknown:
for sym in {a,b,c,d,e,f,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,x,y,z} do solve({LambertW(ln(g)) = ln(sym)}, g) end do;

Clearly a bug and also prsent in Maple 2016.
I shall submit an SCR.


 

@GoitaHass You are not using the code I gave you in your attached worksheet. Your code contains several syntactical errors. I wasn't blunt enough when I wrote: Assuming that your 2-D input can be interpreted to mean the same as this corrected 1-D version ..

Try to take a copy of my reply above and paste it into a simple text editor like NotePad in Windows. You can make Maple work like that.
Since you are new to Maple you may not be aware of the important difference between 2D input and 1D input (aka Maple input).

Go to the menu Tools/Options/Display/Input display choose Maple Notation.
Keep the Options window open.
After that in the Options window go to the tab Interface/Default format for new worksheets choose Worksheet.
Finally click the button Apply Globally.

This action can always be reversed.

Let me add that my personal choice would be to choose simpler names as in this modified version:
restart;
ode := mu1*E1(x)-mu2*(u(x)-d1*E1(x))/d2+diff(gamma1*E1(x)-gamma2*(u(x)-d1*E1(x))/d2, x) = 0;
isc:=E1(0) = 0;
dsolve({ode,isc},E1(x));

@John Fredsted Will this one work in your situation?

conv:=proc(u) local g, res;
  res:=evalindets(u,`*`,s->g(selectremove(type,s,{identical(tau),identical(f(t))})));
  res:=subs(tau*f(t)=f(-t),res);
  eval(%,g=`*`)
end proc;

conv(expr);
conv(tau*f(t)+6*f(t)-(1+7*I)*tau*f(t));
conv([expr,tau*f(t)+6*f(t)-(1+7*I)*tau*f(t)]);

#But maybe just evalindets with algsubs?

evalindets([expr,tau*f(t)+6*f(t)-(1+7*I)*tau*f(t)],`*`,s->algsubs(tau*f(t)=f(-t),s));

## Well, maybe I'm not quite getting it: You probably have many different functions f?
## That could be handled as in this example:
conv:=proc(u) local g, res, tps,S1,S; global tau,t,f,F,h;
  S1:={f(t),F(t),h(t)}; #Just an example
  tps:=identical~({tau} union S1);
  S1:=convert(S1,list);
  S:=tau*~S1=~eval(S1,t=-t);
  res:=evalindets(u,`*`,s->g(selectremove(type,s,tps)));
  res:=eval(res,S);
  eval(%,g=`*`)
end proc;
### And a version with algsubs combined with foldr and evalindets:
L:=[f(t),F(t),h(t)];
S:=tau*~L=~eval(L,t=-t);
conv:=u->foldr(algsubs,u,op(S));
evalindets([expr,tau*f(t)+6*h(t)-(1+7*I)*tau*F(t)],`*`,conv);

@John Fredsted You write that tau is supposed to be a time-reversal operator acting on some time-dependent function f(t).
Doesn't that mean that the `*` is not multiplication in your actual case, and the one you showed us is only a toy example?

@John Fredsted I realized my mistake before your reply. I have edited my answer.
Actually it is the fact that
subs(a*b=4,a*b*c);
eval(a*b*c,a*b=4);

both work as you intended that surprised me.

@dharr Yes, putting uneval quotes around the procedure name is nice.

@vv The assume project is quite ambitious. It is clearly very difficult.
I don't favor ad hoc solutions to satisfy the crowd (or just me) and I think it is fine to have high ambitions.
Nevertheless, straightforward cases like assume(n = 7) or the implied variety ought to be handled somewhat gracefully, whatever I mean by that.

@Markiyan Hirnyk Yes, assume(n >= 7, n <= 7) is equivalent to assume(n=7), so ought to be handled the same way.

My own simple hack of overloading assuming doesn't handle that because only equalities are handled by eval.
Thus
n assuming n>=0,n<=0;

works as it does without the hack, i.e. it returns n.