On a polynomial identity for n\(\times n\) matrices (Q1825930)
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scientific article; zbMATH DE number 4122158
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a polynomial identity for n\(\times n\) matrices |
scientific article; zbMATH DE number 4122158 |
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On a polynomial identity for n\(\times n\) matrices (English)
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1989
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The authors prove the following remarkable result: the polynomial \[ h_ k=\sum_{\sigma,\tau \in S_ k}(sgn \sigma \tau)x_{\sigma (1)}y_{\tau (1)}...x_{\sigma (k)}y\quad_{\tau (k)} \] is an identity of the ring of \(n\times n\) matrices over a commutative ring with 1 for \(k=2n\) and for no smaller value of k. It is an answer to a question of E. Formanek.
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polynomial
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identity
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ring of n\(\times n\) matrices
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