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Re: derivative of matrix in mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120154] Re: derivative of matrix in mathematica
*From*: Bill Rowe <readnews at sbcglobal.net>
*Date*: Sun, 10 Jul 2011 05:01:28 -0400 (EDT)
On 7/9/11 at 7:32 AM, physics1389 at yahoo.com (yashar) wrote:
>in mathematica
>how i can produce a general n by n matrix so that each of its elements be a variable of t???
Any number of ways. It depends on what it is you want. An couple
of examples would be:
In[1]:= m = t RandomInteger[5, {2, 2}]
Out[1]= {{0, 5*t}, {2*t, 0}}
In[2]:= m1 = t^RandomInteger[5, {2, 2}]
Out[2]= {{t, 1}, {t^3, t^2}}
>how i can take derivative of this matrix with respect to variable t?
The same way as taking the derivative of any function with
respect to t. Using the examples above;
In[3]:= D[m, t]
Out[3]= {{0, 5}, {2, 0}}
In[4]:= D[m1, t]
Out[4]= {{1, 0}, {3*t^2, 2*t}}
>how i can with equating this n by n matrix with another n by n matrix which its elements are known obtain unknown elements of this general n by n matrix?
Here, I am not clear on what it is you want to do. I can find a
solution by setting corresponding elements equal as follows
In[5]:= y = RandomInteger[5, {2, 2}];
MapThread[Solve[#1 == #2, t] &, {Flatten@y, Flatten@m}]
Out[6]= {{}, {{t -> 1}}, {{t -> 2}}, {{}}}
But it is trivial to find examples where this won't work.
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