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Preprint
Commutators, matrices and an identity of Copeland
arXiv (Cornell University)
24 Aug 2019
Abstract
Given two elements $a$ and $b$ of a noncommutative ring, we express $\left(
ba\right)^n$ as a "row vector times matrix times column vector" product, where
the matrix is the $n$-th power of a matrix with entries
$\dbinom{i}{j}\operatorname{ad}_a^{i-j}\left( b\right)$. This generalizes a
formula by Tom Copeland used in the study of Pascal-style matrices.
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Details
- Title
- Commutators, matrices and an identity of Copeland
- Creators
- Darij Grinberg
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862236704721