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Results tagged with block-matrices
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user 1306
4
votes
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Solving a recursion for polynomials defined by a matrix product
Your polynomial is precisely
$$
\sum_{k_1+2k_2+\cdots+nk_n=n}\binom{k_1+\cdots+k_n}{k_1,\ldots,k_n}X_1^{k_1}\cdots X_n^{k_n}.
$$
The proof is straightforward by induction: you have
$$
p_n(X)=\sum_{i= …
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