6
$\begingroup$

I want to construct a Toeplitz matrix in Mathematica. Usually it is done in Mathematica using the following command:

ToeplitzMatrix[{a,b,...},{a,y,...}]

I want to have the first and the second list like {a,b,...} and {a,y,...} above to each contain N elements for a given number N (say 5 or 6; I want to keep the option of changing it). I want a=0. From b onwards I want to have (-1)^n nx (starting with n=1) and from y onwards -(-1)^n nx alternatively.

So at the end, it should look like \begin{pmatrix} 0\quad x\quad -2x\quad\dots\\ -x\quad 0\quad x\quad \dots\\ 2x\quad -x\quad 0\quad \dots\\ \dots \end{pmatrix}

I am quite new to all the powers of Mathematica. So some help will be greatly appreciated.

$\endgroup$
0

1 Answer 1

5
$\begingroup$
tf[nn_] := With[{n = Range[0, nn]}, ToeplitzMatrix[(-1)^n n x, -(-1)^n n x]]

For the question in the comment:

tf2[nn_] := 
 With[{n = Range[0, nn]}, 
  Module[{expr = (-1)^n Cot@(n x)}, expr[[1]] = 0; ToeplitzMatrix[expr, -expr]]]

tf3[nn_] := 
 With[{n = Range@nn}, 
  With[{expr = Join[{0}, (-1)^n Cot@(n x)]}, ToeplitzMatrix[expr, -expr]]]
$\endgroup$
7
  • $\begingroup$ Sorry, but it says: $\endgroup$
    – Student
    Jan 28, 2016 at 14:39
  • $\begingroup$ "Objects of unequal length in {1,-1,1,-1,1}\ {0,1,2,3,4}\ {[Pi]/12,\ [Pi]/6,[Pi]/4,[Pi]/3,(5\[Pi])/12,[Pi]/2,(7\[Pi])/12,(2\[Pi])/3,\ (3\[Pi])/4,(5\[Pi])/6,(11\[Pi])/12,[Pi],(13\[Pi])/12,(7\[Pi])/6,\ (5\[Pi])/4,(4\[Pi])/3,(17\[Pi])/12,(3\[Pi])/2,(19\[Pi])/12,(5\[\ Pi])/3,(7\[Pi])/4,(11\[Pi])/6,(23\[Pi])/12,2\ [Pi]} cannot be \ combined" $\endgroup$
    – Student
    Jan 28, 2016 at 14:39
  • $\begingroup$ Also, here the first element 0 is obtained just by putting 0 for n in (-1)^n nx. But what if I have 0 for the diagonals and say (-1)^n cot(nx), so that I really need to put a second rule for the diagonals? $\endgroup$
    – Student
    Jan 28, 2016 at 14:41
  • 1
    $\begingroup$ @Student You forgot to Clear[x] $\endgroup$
    – xzczd
    Jan 28, 2016 at 14:41
  • $\begingroup$ Sorry, it is working for what you said. But for the other one I mentioned, I can't do e.g. tf[nn_] := With[{n = Range[0, nn]}, ToeplitzMatrix[{0,(-1)^n Cot[n x]}, {0,-(-1)^n Cot[n x]}]]. $\endgroup$
    – Student
    Jan 28, 2016 at 14:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.