Hi,
My question is the following.
suppose I have block matrices:
A={{a,0},{0,0}};
B={{b,0},{0,0}};
C={{c,0},{0,0}};
Is there a way to tell Mathematica that a,b and c are some square matrices (say 3 by 3) so that the output of Tr[A.B.C] is something like Tr[a.b.c] instead of just abc?
Thanks in advance,
Diego
Hi Diego,
What do you mean with Tr. The trace of the transpose? Furthermore the variable ‘C’ is protected in Mathematica, it has a very special purpous. Always try to use small letters. What do you mean with the ‘,’ do you mean dot-product? Please clarify what you want. The trace (the sum of the diagonal row) can be obtained by using Total[Diagonal].
Hi Sander,
Sorry I wasn’t very careful in writing my question. so let me rephrase it. Yes by “Tr” I mean the trace and by “.” the dot product. If I write:
mata = {{a, 0}, {0, 0}};
matb = {{b, 0}, {0, 0}};
matc = {{c, 0}, {0, 0}};
And then
Tr[mata.matb.matc]
Tr[matb.mata.matc]
The output is
a b c
a b c
which is fine if a,b and c are numbers. However, if they are matrices, then in general Tr[a.b.c] and Tr[b.a.c] are different. So I would like to keep track of this, without having to define a, b and c.
ArrayFlatten will do the job.
a = RandomInteger[5, {3, 3}];
b = RandomInteger[5, {3, 3}];
f = RandomInteger[5, {3, 3}];
MatrixForm /@ {a, b, f}
A = {{a, 0}, {0, 0}};
B = {{b, 0}, {0, 0}};
F = {{f, 0}, {0, 0}};
MatrixForm[ArrayFlatten[#]] & /@ {A, B, F}
Now check:
In[]:= a.b.f // Tr
Out[]= 809
In[]:= ArrayFlatten[A].ArrayFlatten[B].ArrayFlatten[F] // Tr
Out[]= 809
Thank you for your help!