I need to write in mathematica programming language a matrix Laurent Polynomial $$ T = \sum_{i=-5}^{5} A_i t ^i $$ where the $A_i$ are $n \times n$ matrices (I want the entries to be symbolic) which can take entries in $\mathbb{C}$. So that I can get the conditions on the entries of the $A_i$ such that $T^2$ and $T^3$ are just polynomials in $\mathbb{C}[t^2,t^3]$.
1 Answer
$\begingroup$
$\endgroup$
For convenience, first define a function that creates the Ai with symbolic elements:
n = 2;
A[i_] := Array[(Subscript[a[i], #1, #2]) &, {n, n}]
The rest is trivial, simply sum it up:
Sum[A[i] t^i, {i, -5, 5}]
An example for n=2. Note that result is a matrix where every element is a Laurent series:
Sum
? $\endgroup$Array[a, {11, n, n}] . t^Range[-5,5]
, perhaps, assumingn
is a positiveInteger
. There a bias in the index $i$: $(A_i)_{rc}$ is represented bya[i+6, r, c]
. $\endgroup$Dot
needs to be reversed in MichaelE2's answer; also note that you can eliminate the bias/offset by taking advantage of the second argument ofArray
, which gives the starting indices:(t^Range[-5, 5]) . Array[a, {11, n, n}, {-5, 1, 1}]
$\endgroup$