An elementary proof of the theorem that the most general matrix commutative with a given \(n\)-rowed square matrix involves at least \(n\) arbitrary parameters. (Q2616617)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary proof of the theorem that the most general matrix commutative with a given \(n\)-rowed square matrix involves at least \(n\) arbitrary parameters. |
scientific article |
Statements
An elementary proof of the theorem that the most general matrix commutative with a given \(n\)-rowed square matrix involves at least \(n\) arbitrary parameters. (English)
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1934
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Der im Titel der Arbeit angegebene Satz wird elementar bewiesen, d. h. nur unter Anwendung rationaler Operationen auf die Koeffizienten der vorgegebenen Matrix. Der Grundgedanke ist folgender: Die Vertauschbarkeitsbedingung führt auf ein System von \(n^2\) linearen Gleichungen; es wird dann gezeigt, daß der Rang dieses Systems \(n^2-n\) nicht überschreiten kann, was offenbar mit der Behauptung gleichwertig ist.
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